Microfluidic chemostat

ABSTRACT

A chemostat is described that includes a growth chamber having a plurality of compartments. Each of the compartments may be fluidly isolated from the rest of the growth chamber by one or more actuatable valves. The chemostat may also include a nutrient supply-line to supply growth medium to the growth chamber, and an output port to remove fluids from the growth chamber. Also, a method of preventing biofilm formation in a growth chamber of a chemostat is described. The method may include the steps of adding a lysis agent to a isolated portion of the growth chamber, and reuniting the isolated portion with the rest of the growth chamber.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/197,654, filed Aug. 3, 2011, titled “MICROFLUIDIC CHEMOSTAT” which isa continuation of U.S. patent application Ser. No. 12/182,088, filedJul. 29, 2008, titled “MICROFLUIDIC CHEMOSTAT,” which is a divisional ofU.S. patent application Ser. No. 11/012,852, filed Dec. 14, 2004, titled“MICROFLUIDIC CHEMOSTAT,” which claims the benefit of U.S. ProvisionalApplication No. 60/536,863, filed Jan. 16, 2004, titled “MICROFLUIDICCHEMOSTAT” the entire disclosures of which are herein incorporated bythis reference.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSOREDRESEARCH OR DEVELOPMENT

This material is based upon work supported by the Defense AdvancedResearch Projects Agency (Grant No. N66001-02-1-8929), and the NationalScience Foundation under Grant No. CTS.0088649. The U.S. Government maytherefore have certain rights in the invention.

BACKGROUND OF THE INVENTION

The chemical complexity of pharmaceutical proteins makes it difficult toproduce them synthetically for medical treatments. For many of theseproteins, the only practical production route is to grow bacterialcultures that have been designed to produce the protein in adequatequantities. Thus, pharmaceutical manufacturers, among others, have anactive interest in developing devices and methods for the study ofbacterial cultures. One technique for measuring the size and growth rateof bacterial cultures involves counting bacteria colonies using plating,which relies on the colony-forming ability of viable cells. A sample ofan appropriately diluted culture is dispersed on a solid medium and thenumber of colonies that form is determined. Unfortunately, plating canproduce inexact measurements because the culture continues to grow at anunknown rate during the period of dilution in preparation for plating.In another technique, the total number of cells can be determinedmicroscopically by determining the number of cells per unit area in acounting chamber (a glass slide with a central depression of knowndepth, whose bottom is ruled into squares of known area). However, thistechnique is a hands-on, serial process that is prone to human error.

Counting errors may be reduced by using electronic counting devices,such as a coulter counter, which can determine the size distribution aswell as the number of bacteria in a sample culture of known volume. Thecoulter counter relies on a pore, through which a known volume ofsuspension is pumped. Although the counter is rapid and accurate, it isalso expensive and subject to a number of artifactual complications.Moreover, the pore through which the suspension is pumped is prone toclogging if the media and diluents are not carefully prepared.

Another technique for studying and measuring bacterial cultures involvesdetermining the dry weight of cells in a known volume of suspension.This technique is time consuming and requires a considerable amount ofsacrificial culture. As such, it is unsuitable for routine monitoring ofthe growth rate. Optical density has also been used to determine growthrates using cell density. However, the correlation between cell densityand optical density of the culture may change during production ofproteins that aggregate and form inclusion bodies.

Chemostats may also be used to study and measure bacterial cultures.These devices can maintain a constant population of bacteria in a stateof active growth. This may be done by periodically substituting afraction of a microbial culture with an equal volume of fresh, sterile,chemically defined growth medium. The influent composition may be suchthat the ingredients are in optimal amounts except for thegrowth-limiting factor, whose concentration is kept sufficiently low. Atan adequate flow rate, a low concentration of the growth-limiting factorestablishes itself in the growth chamber.

At sufficiently low concentrations of the growth-limiting factor themicrobial growth rate is directly proportional to the concentration ofthe growth-limiting factor and independent of other nutrient factors, aswell as bacterial metabolites. The bacterial population mayautomatically proceed towards a steady state of growth, where the celldensity remains constant and the growth rate is sufficient to replacethe cells lost in the effluent. The steady-state cell concentration maybe varied by changing the dilution rate, or the concentration of thegrowth-limiting factor in the influent.

Data collection with conventional chemostats is not easy to automate,which makes studies and measurements of the bacterial cultures laborintensive. The devices also consume large amounts of growth medium thatincrease the cost of experiments, especially when costly reagents haveto be used.

Another difficulty with chemostats is their tendency to form biofilms ongrowth-chamber walls and probe surfaces. The biofilms can start whenmicroorganisms (e.g., bacteria from the culture) attach to a wall orprobe surface during the course of chemostat operation. Once started,the biofilms are difficult to remove and may consume a significantfraction of the substrate. This may compromise the fixed biomassfundamental conservation principle of the chemostat, inducing hybridbatch/chemostat characteristics. The significance of this artifact maybe magnified in laboratory scale chemostats where the surface area tovolume ratio is large. Thus there remains a need for chemostattechnology that suppresses or prevents biofilm growth, and consumessmaller amounts of growth medium, among other characteristics.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the invention include a chemostat. The chemostat mayinclude a growth chamber having a plurality of compartments, where eachof the compartments may be fluidly isolated from the rest of the growthchamber by one or more actuatable valves. The chemostat may also includea nutrient supply-line to supply growth medium to the growth chamber,and an output port to remove fluids from the growth chamber.

Embodiments of the invention may also include a chemostat chip. Thechemostat chip may include an array of chemostats, where each of thechemostats includes a growth chamber having a plurality of compartments,where each of the compartments may be fluidly isolated from the rest ofthe growth chamber by one or more actuatable valves. The chemostats mayalso include a nutrient supply-line to supply growth medium to thegrowth chamber, and an output port to remove fluids from the growthchamber.

Embodiments of the invention may further include a method of making achemostat. The method may include the step of forming a flow layercomprising a flow channel, where a growth chamber of the chemostatincludes the flow channel. The method may also include coupling the flowlayer between a first control layer and a second control layer, whereeach of the control layers includes one or more control channels thatcan be actuatued to fluidly isolate a compartment of the flow channel.

Embodiments of the invention may also further include a method ofpreventing biofilm formation in a growth chamber of a chemostat. Themethod may include the steps of adding a lysis agent to a isolatedportion of the growth chamber, and reuniting the isolated portion withthe rest of the growth chamber.

Additional embodiments and features are set forth in part in thedescription that follows, and in part will become apparent to thoseskilled in the art upon examination of the specification or may belearned by the practice of the invention. The features and advantages ofthe invention may be realized and attained by means of theinstrumentalities, combinations, and methods described in thespecification.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a chemostat according to an embodiment of the invention;

FIG. 2 shows a flowchart including steps for a chemostat cleaning methodaccording to embodiments of the invention;

FIG. 3 shows a chemostat chip according to an embodiment of theinvention;

FIG. 4 shows a flowchart of a method of making a chemostat chipaccording to an embodiment of the invention;

FIGS. 5A-B show bacterial culture growth curves taken during experimentsusing a chemostat system according to the invention;

FIG. 6 shows a plot of Tau I versus the dilution rate from experimentsrun using a chemostat system according to the invention; and

FIG. 7 shows a plot of steady state cell concentrations versus thedilution rate from experiments run using a chemostat system according tothe invention.

FIG. 8 is an illustration of a first elastomeric layer formed on top ofa micromachined mold;

FIG. 9 is an illustration of a second elastomeric layer formed on top ofa micromachined mold;

FIG. 10 is an illustration of the elastomeric layer of FIG. 9 removedfrom the micromachined mold and positioned over the top of theelastomeric layer of FIG. 8;

FIG. 11 is an illustration corresponding to FIG. 10, but showing thesecond elastomeric layer positioned on top of the first elastomericlayer.

FIG. 12 is an illustration corresponding to FIG. 11, but showing thefirst and second elastomeric layers bonded together.

FIG. 13 is an illustration corresponding to FIG. 12, but showing thefirst micromachined mold removed and a planar substrate positioned inits place.

FIG. 14A is an illustration corresponding to FIG. 13, but showing theelastomeric structure sealed onto the planar substrate.

FIG. 14B is a front sectional view corresponding to FIG. 14A, showing anopen flow channel.

FIG. 14H shows a first flow channel closed by pressurization of a secondflow channel.

FIGS. 14C-14G are illustrations showing steps of a method for forming anelastomeric structure having a membrane formed from a separateelastomeric layer.

FIGS. 15A and 15B illustrates valve opening vs. applied pressure forvarious flow channels.

FIG. 16 illustrates time response of a 100 μm×100 μm×100 μm RTVmicrovalve.

FIG. 17 illustrates a cross-sectional view of a flow-channel through apair of flow channels.

FIG. 18 illustrates a cross-sectional view of a flow channel with acurved upper wall.

FIG. 19A is a top schematic view of an on/off valve.

FIG. 19B is a sectional elevation view along line 30B-30B in FIG. 19A.

FIG. 20A is a top schematic view of a peristaltic pumping system.

FIG. 20B is a sectional elevation view along line 31B-31B in FIG. 20A

FIG. 21 is a graph showing experimentally achieved pumping rates vs.frequency for an embodiment of the peristaltic pumping system of FIG.20.

FIG. 22A is a top schematic view of one control line actuating multipleflow lines simultaneously.

FIG. 22B is a sectional elevation view along line 33B-33B in FIG. 21A

FIG. 23 is a schematic illustration of a multiplexed system adapted topermit flow through various channels.

FIG. 24A is a plan view of a flow layer of an addressable reactionchamber structure.

FIG. 24B is a bottom plan view of a control channel layer of anaddressable reaction chamber structure.

FIG. 24C is an exploded perspective view of the addressable reactionchamber structure formed by bonding the control channel layer of FIG.24B to the top of the flow layer of FIG. 24A.

FIG. 24D is a sectional elevation view corresponding to FIG. 24C, takenalong line 25D-25D in FIG. 24C.

FIG. 25 is a schematic of a system adapted to selectively direct fluidflow into any of an array of reaction wells.

FIG. 26 is a schematic of a system adapted for selectable lateral flowbetween parallel flow channels.

FIG. 27A is a bottom plan view of first layer (i.e.: the flow channellayer) of elastomer of a switchable flow array.

FIG. 27B is a bottom plan view of a control channel layer of aswitchable flow array.

FIG. 27C shows the alignment of the first layer of elastomer of FIG. 27Awith one set of control channels in the second layer of elastomer ofFIG. 27B.

FIG. 27D also shows the alignment of the first layer of elastomer ofFIG. 27A with the other set of control channels in the second layer ofelastomer of FIG. 27B.

FIGS. 28A-28J show views of one embodiment of a normally-closed valvestructure in accordance with the present invention.

FIGS. 29A and 29B show plan views illustrating operation of oneembodiment of a side-actuated valve structure in accordance with thepresent invention.

FIG. 30 shows a cross-sectional view of one embodiment of a compositestructure in accordance with the present invention.

FIG. 31 shows a cross-sectional view of another embodiment of acomposite structure in accordance with the present invention.

FIG. 32 shows a cross-sectional view of another embodiment of acomposite structure in accordance with the present invention.

FIGS. 33A-33D show plan views illustrating operation of one embodimentof a cell pen structure in accordance with the present invention.

FIGS. 34A-34B show plan and cross-sectional views illustrating operationof one embodiment of a cell cage structure in accordance with thepresent invention.

FIGS. 35A-35B show plan views of operation of a wiring structureutilizing cross-channel injection in accordance with the embodiment ofthe present invention.

FIGS. 36A-36D illustrate cross-sectional views of metering by volumeexclusion in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Chemostats of the present invention include microfluidic chemostatshaving growth chambers divided into two or more compartments. Thesechemostats can operate with low quantities of growth reagents/medium,which reduces the costs of the chemostat experiments. They may also beoperated such that discrete cleaning of the chemostat compartments canoccur while an experiment is being conducted, which reduces or preventsthe formation of biofilms on the walls of the device.

The small size of the microfluidic chemostats of the invention have highsurface area to volume ratio (e.g., about 100 times the surface area tovolume ratio of a conventional chemostat). The high ratio permits alarger percentage of the growth chamber surface (e.g., about 55% of thesurface or more) to serve as a diffusion interface for the diffusion ofgases such as oxygen (O₂) and carbon dioxide (CO₂). The gas diffusionmay be further enhanced by constructing the growth chamber out ofmaterials that have high gaseous permeability (e.g., silicone elastomerssuch as polydimethylsiloxane (PDMS), which is commercially available asGeneral Electric RTV 615). Using high gaseous permeability materials inthe chemostat may help provide a higher level of aeration, which canreduce media acidification and the concentration of toxic metabolitesthat are attributed to the incomplete oxidation of carbon sources athigh cell densities. By reducing the acidity and metaboliteconcentration of the bacterial growth medium, bacterial cell growth maybe less inhibited than in conventional chemostats or batch cultures.

The chemostats of the invention may be operated in a non-continuousmode, such that dilutions may be performed in discrete steps. In adiscrete lysing step, one of the compartments is fluidly isolated fromthe rest of the growth chamber and exposed to a lysis buffer containinga lysing agent that kills the cells in the compartment, including anycells attached to the chamber walls that could grow a biofilm. The lysisbuffer may then be removed and fresh growth medium added to thecompartment before it rejoins the rest of the growth chamber. Isolatingthe compartment during the lysing step prevents all the cells in thegrowth chamber from being exposed to the lysis buffer at once. Instead,the cleaning and dilution that occurs in the discrete lysing stepdecreases the cell population by a percentage that is about equal to theratio of the volume of the cleaned chamber to the total volume of thegrowth chamber. For example, if the growth chamber is divided into 16equal volume compartments, then cleaning one chamber in a lysing stepwill dilute the total cell population by 1/16th. Even with a dilutionfraction this size or larger, the microfluidic microbialdiscretized-flow system should reach a steady state.

The chemostats of the present invention may be used in a variety ofbacterial culture applications, including the study of bacterialmicrobes. The studies may include examination and measurement ofmicrobial metabolism, regulatory processes, adaptations and mutations,among others. Studies may also be done on how bacterial microbes respondto changes in their environment. The chemostats can facilitate thecharacterization of microbial response to changes in specificenvironmental factors by providing constant environmental conditions forgrowth and product formation, as well as facilitating the determinationof growth conditions that optimize biochemical processes such aspharmaceutical protein production. From such studies, it may be possibleto reconstruct the general behavior of microorganisms in their nativeconditions. The well controlled growth conditions and ability to make insitu optical studies of self sustaining communities of a few thousandbacteria provided by the chemostats of the present invention are alsouseful for studies of genetic regulatory networks, microbial ecosystems,and artificial biological circuits, among other applications.

The chemostats of the present invention also make it possible todetermine as well as maintain growth conditions that enhance theproductivity or yield of biochemical processes including, for example,pharmaceutical proteins production, and biochemical biotransformation.The small footprint, parallel architecture, and low reagent consumptionof the microfluidic chemostats can make them an efficient tool for highthroughput screening applications ranging from chemical genetics topharmaceutical discovery.

Small-scale inexpensive chemostats that control biofilm growth canfacilitate selection-pressure-driven screening of cell populations. Theuniform environment in the chemostats subject their microbial populationto strong selection pressures, which, because of spontaneous mutations,may result in the appearance of mutants with qualities (e.g., improvedgrowth-rate, nutrient uptake, ability to degrade toxic refractorycompounds, etc.) superior to those of their ancestors. The chemostatsmay also be used for industrial microbial studies to understand thetoxicity, carcinogenicity and degradability of complex substrates suchas crude hydro-carbons, pesticides and sewage. Kinetic data obtainedfrom such devices would also be scalable to that of large-scalebioreactor experiments, where wall-growth effects are not significant.Additional details of embodiments of chemostats according to theinvention will now be described.

Exemplary Chemostat

Referring now to FIG. 1, a chemostat according to an embodiment of theinvention is shown. The chemostat includes a growth chamber 102 thatincludes 16 compartments 104, each of which may be fluidically isolatedfrom rest of the growth chamber 102 by actuatable valves 106. Growthmedium may be circulated through the growth chamber 102 with the help ofperistaltic pump 108 to keep the growth medium well mixed.

In this embodiment, the growth chamber 102 is a planar loop fluidchannel having a total volume on the order of tens of nanoliters (e.g.,about 16 nL). The nanoliter volume growth chamber 102 allows thebacterial culture to be monitored in situ by optical microscopy (notshown). This monitoring can provide an automated real time measurementof cell density and morphological properties of the bacterial culturewith single cell resolution. The chemostat may be automated to operateautonomously for up to a week or longer, creating a stable steady statebacteria culture having about 10⁵ cells in a reactor volume millions oftimes smaller than conventional batch reactors, and media consumption ofabout 40 microliters/day or less. The automated device may include anautomated microscope reader (not shown) that provides real-time,non-invasive sampling and documentation of microbial properties, such asthe total cell count and cell morphology of the bacterial culture.

As the volume of the growth chamber of a chemostat shrinks, its surfacearea to volume ratio increases. Consequently, biofilm growth exerts aproportionately larger influence on the kinetics. In the presentinvention, biofilm growth may be prevented (or suppressed) by segmentingthe chemostat into individually addressable compartments that can beperiodically cleaned with a lysis buffer to thwart biofilm formation.Preventing biofilm formation (i.e., zero wall-growth) makes possible thebasic reduction of chemostat growth equations to an ideal monotonesystem, simplifying the analysis of chemostat-like behavior.

In the chemostat embodiment shown in FIG. 1, the growth-chamber 102 iscomposed 16 individually addressable, equal volume compartments 104. Oneof the compartments 104 may be isolated from the rest of chamber 102 byclosing actuatable valves 106. Lysis buffer may be supplied to thecompartment 104 through a supply channel 110 that is fluidly coupled toa lysis buffer source inlet 109. Growth medium may also be provided tothe compartment 104 from a growth medium inlet 107. Waste materials maybe removed from the growth chamber 102 through one of the waste outlets114 a-c.

Embodiments include a periodic, sequential cleaning and rinsing adjacentcompartments to prevent biofilm growth on the inner wall of the growthchamber 102. When the compartment 104 rejoins the growth chamber, thebacterial culture in chamber 102 will be diluted by 1/16th (i.e., theratio of the compartment 104 volume to the total volume of growthchamber 102).

FIG. 2 shows a flowchart that includes steps for a chemostat cleaningmethod according to embodiments of the invention. The method includesthe discrete lysing of individual compartments of the growth chamber ofthe chemostat. The discrete lysing includes fluidly isolating anindividual compartment from the rest of the growth chamber at step 202by closing valves at opposite ends of the compartment. The fluidlyisolated compartment may be connected to a supply channel and an outputchannel, where the supply valve is opened to introduce lysis buffer tothe compartment at step 204. The lysis buffer may include a lethalbacteria protein extraction reagent (e.g., a commercially availablelysis agent from PIERCE in Rockford, Ill.) that flows through thecompartment for a period of time (e.g., 60 seconds) to flush out thecell suspension and dissolve (lyses) away any cells that might beadhering to the wall. The lysis buffer may then be removed along withthe remains of the cells, by flushing the compartment with fresh sterilegrowth medium for a period of time (e.g., about 60 seconds) at step 206.Once the compartment is rinsed and filled with fresh growth medium,supply channel and an output port may be closed and actuatable valvesreopened to reunite the compartment with the rest of the growth-chamberin step 208. Rotary mixing may be resumed to disperse the influentquickly and uniformly throughout the growth-chamber in step 210.

The discrete flow/sequential lysis cleaning method may be repeatedperiodically during the experiment, using successive compartments asdilution premises. Sequential lysis of the growth chamber compartmentscan provide a periodic chemical cleaning of the growth-chamber over aperiod of time (e.g., about once every three hours) which can suppressor prevent biofilm formation on the surfaces of the chamber. Individualaddressability of the growth chambers coupled with effective fluidicisolation allows for the removal of incipient wall growth in a givencompartment without substantially harming bacteria growth in the rest ofthe growth chamber.

Exemplary Chemostat Chip

The present invention includes arrays of two or more chemostatsincorporated into a chemostat chip 300. FIG. 3 shows 6 chemostats 302organized into a 2×3 array on a microfluidic chemostat chip 300. Duringoperation, multiple chemostat experiments may be run in parallel (i.e.,overlapping in time) on the chemostat chip 300, and an automatedmicroscope reader (not shown) may perform real-time sampling anddocumentation of the microbial properties (e.g., total cell count) foreach experiment. This kind of automated data acquisition reduces thechances of data artifacts caused by human error, and increases the datacollection rate and the temporal resolution of the data recorded duringthe experiment.

The 2×3 array on chemostat chip 300 may have dimensions on the order ofmillimeters (e.g., 20 mm×35 mm×5 mm) and may be fabricated from asilicone elastomer. The chip 300 has six parallelly operable fluidicloop chemostats 302. Each chemostat 302 includes a growth chamber,encircled by a nutrient supply-line that connects to four input portsand an output port. Each of the growth chambers include a hollowround-cornered square strip (11.5 mm perimeter), with rectangularcross-sectional interior geometry (10 μm×140 μm). Situated along thegrowth chamber is a 3-valve peristaltic pump for the rotary mixing ofthe growth chamber contents. The growth chamber loops may have a roundedcross-sectional geometry in the areas that contain valves for fluidicisolation and peristaltic pumping. Umbilical fluidic links may connectthe growth chamber to the supply line at eight strategic locations.Within the perimeter of each of the growth chambers are two ports. Theseports may be 625 μm-diameter holes incorporated into the chip.

The small footprint and parallel architecture of the microfluidic-basedchemostat allows for large-scale screening investigations in twodimensional chemostat arrays. The zero wall-growth aspect of the chip300 makes possible the basic reduction of the chemostat equations to anideal monotone system, simplifying the analysis of chemostat-likebehavior. In the embodiment shown, each chemostat 302 holds an activevolume of about 11 nL, so small quantities of reagents (e.g., growthmedium) are required for the experiments. This significantly reduces theoperational costs for experiments run on the chip 300.

Exemplary Fabrication of Chemostat Chip

Referring now to FIG. 4, a flowchart that includes steps in the methodof making a chemostat chip is shown. The method includes forming a flowlayer in step 402. The flow layer may be fabricated out of the siliconeelastomer polydimethylsiloxane (PDMS) (General Electric RTV 615) usingstandard “multi-layer soft lithography”. The layer may be formed withboth rectangular channel geometry, as well as rounded geometry for valveactuation.

Negative molds for the flow layer may be cast by sequentially byapplying two different types of photoresist. The rectangular channelfeatures may be molded out of a first photoresist material that does notround when annealed (e.g., SU8 2010 from MicroChem Corporation ofNewton, Mass.), while other features of the flow layer may be made froma second photoresist material (e.g., SRJ 5740 from MEMS Exchange inReston, Va.). The first photoresist material may be spun onto a siliconwafer (e.g., a wafer spinning at 3,000 rpm for 60 sec) to create a 10 μmthick layer and patterned using negative high-resolution transparencymasks. The second photoresist material may be spun onto the same siliconwafer (e.g., spinning the wafer at 2,200 rpm for 60 sec) to create a 10μm thick layer and patterned using positive high-resolution transparencymasks, aligned to fit the patterns formed in the first photoresistmaterial. The two-photoresist hybrid mold may then be annealed at 120°C. for 20 minutes to achieve rounded channel geometry for the featuresin the channels of the second photoresist material while preserving therectangular geometry of the features in the first photoresist material.

The fabrication method also includes forming a first and second controllayer in step 404, and then coupling the flow layer between the controllayers in step 406. The control layers have distinct functionalities atdifferent regions of each fluidic module for controlling flow, rotarymixing, and fluidic isolation within the growth chamber of each chemstatin the array. At each junction between a control and fluid line, thereexists a thin membrane, which can be deflected by hydraulic actuation ofthe control channel to close the flow channel, creating a valve. Threevalves in a row may be used to form a peristaltic pump for circulatingfluids in the growth chambers.

The control and fluid layers of the chip may be cast from separate moldsthat are patterned on silicon wafers with photolithography. Negativemolds for features of the control layers may be fabricated from aphotoresist (e.g., AZ PLP 100 XT photoresist from Clariant Corporation,Somerville, N.J.). The photoresist may be spun onto silicon wafers at1,200 rpm for 60 sec to create a 30 μm thick layer and patterned usingpositive high-resolution transparency masks.

Additional details on the formation of microfabricated fluidic devicesutilizing elastomer materials will be described following a discussionof some experiments that were conducted using chemostat systemsaccording to embodiments of the invention.

EXPERIMENTAL

Experiments were conducted using chemostats according to embodiments ofthe invention to characterize the behavior of Escherichia Coli bacteriaat different dilution rates and influent compositions.

Steady-state behavior of E. Coli cultures were investigated with thechemostats, including the measurement and modeling of growth ratemodulation by nutrient availability, taking into account the effects oftoxic metabolite accumulation. Studies have shown that nutrientdepletion and toxic metabolite accumulation are not the only factorsresponsible for the transition from the exponential to the stationaryphase in Escherichia Coli cultures. Quorum-sensing mechanisms(cell-associated sensing) have also been found to be importantregulators of cell division and density, even under non-limiting (albeitdeclining) nutrient concentrations. In other words, in the presence ofnon-limiting albeit declining nutrient concentrations, E. Coli bacteriaadjust their own growth rate in response to their cell density through acell-associated sensing mechanism capable of steering a bacterialculture from the exponential to the stationary growth phase. This may behow the bacteria population economizes nutrient consumption to preservemetabolic energy and maximize the period of culturability afterretirement into the stationery phase.

Chemostat experiments were performed using E. coli bacteria growing oncomplex (LB) medium. A model that was consistent with our experimentalmeasurements suggested that steady-state nutrient concentrations werenot in the limiting regime. This would attribute the establishment ofsteady-state in the chemostats to a cell-density dependent mechanismother than toxic metabolite accumulation. This provides evidence ofgrowth limitation by the aforementioned cell-associated sensingmechanism. The experiments with the chemostats suggest a reliance oncell-associated sensing instead of nutrient limitation to establishsteady-state growth. Details about the chemostat system will now bedescribed.

Chemostat System:

The microfluidic chemostat system used for the experiments is equippedwith a non-invasive automatic online cell density analyzer, which allowsfor simultaneous monitoring of six micro-chemostats (about 10 nL each)on a single chip, and provides high temporal resolution. The chemostatis refined to operate with zero microbial wall growth. The microfluidicchips are fabricated from a silicone elastomer according to standardsoft-lithography techniques. We attribute the ability of bacteria tothrive in these devices to the high gaseous permeability of the siliconeelastomer as well as an about 100 fold increase in the growth chambersurface area to volume ratio.

Bacterial Strain:

Experiments included the use of E. Coli strain MG1655, and the Dh5αstrain that expresses lad. These strains were received from Dr. UriAlon.

Preculture:

Luria-Bertani (LB) medium contained Bacto Yeast Extract (5 gL⁻¹;Beckton, Dickinson and company, Sparks, Md.), Bacto Tryptone (10 gL⁻¹;Becton, Dickinson and Company, Sparks, Md.), NaCl (10 gL⁻¹; MallinckrodtLaboratory Chemicals, Phillipsburg, N.J.), Bovine Serum Albumin (5 gL⁻¹;Sigma Aldrich, St. Louis, Mo.) as an anti-adhesion adjuvant andkanamycin (30 μg/ml), as an antibiotic. Cultures (1 ml) inoculated fromfrozen stock were grown for six hours at 37° C. with shaking at 280 rpm.In additional experiments, a MOPS EZ rich medium was used that included10% (v/v) MOPS mixture, 1% (v/v) 0.132M K₂HPO₄, 10% (v/v) ACGUsupplement, 20% (v/v) supplement EZ and 11 mM glucose (TekNova Inc.,Half Moon Bay, Calif.).

Chemostat Culture:

Chemostat cultures (standard volume 11 nL, temperature 21° C., pH 7)were inoculated with the preculture to about 5 bacteria μL⁻¹. The LBmedium was used with the concentration of bacto tryptone adjusted to 3μL⁻¹, 0.5 gL⁻¹, and 0.1 gL⁻¹. In additional experiments, chemostatcultures with standard volumes of 16 nL, temperatures of 21° C. or 37°C., and pH 7 were inoculated with the preculture to about 20 bacteriaμL⁻¹. The same LB medium was used.

The Microfluidic Chemostat Reader:

A microfluidic chemostat reader was assembled to facilitate theautomated experiment control, data acquisition and data processing. Itwas a multi-component system consisting of a Nikon TE 2000 (A. G. HeinzeInc., Lake Forest, Calif.) inverted microscope furnished with a PRIORScientific XYZ motorized stage system (A. G. Heinze Inc., Lake Forest,Calif.). Imaging was done using a 40× dry Nikon objective or a PlanFluor 40×0.75NA ph2 DLL objective. The images were taken by acharge-coupled device (CCD) camera and recorded by a PXC200 color framegrabber (Cyberoptics Semiconductor, Beaverton, Oreg.). We developedalgorithms that were implemented in Labview software to control thesynchronized operation of these ingredient components (as well as otherchip operation functions).

Microscopic Counting:

The chemostat architecture was such that all the bacterial cells wereconfined in a growth chamber 10 μm high, which is the equivalent of asingle focal plane. As such, the total number of cells in each chemostatwas determined through automated microscopy by counting the number ofcells present in a growth chamber section of known volume. A set of 9still images was taken at a given location of the chemostat,rotary-mixing the growth-chamber contents in-between consecutivesnapshots. We developed image-processing algorithms (implemented inMatlab) to determine the average number of cells in the set of picturestaken, from which the total cell count could be extrapolated. Themotorized stage system allowed for the simultaneous documentation ofmultiple chemostat experiments running in parallel on the chip.

40 experimental runs were performed in 5 different chips using a varietyof growth media (MOPS EZ RICH and LB broth with various concentrationsof glucose and bacto-trptone respectively) at 21° C. or 37° C. Table 1summarizes the experiment conditions for the experiments.

TABLE 1 Growth Plots Over Time for Various Growth Media and DilutionRates Plot No. Growth Medium Dilution Rate Temperature 1 MOPS, 0.11 nM0.35 hr⁻¹ 37° C. glucose 2 MOPS, 0.11 nM 0.31 hr⁻¹ 37° C. glucose 3 LB,0.5 g/L bacto- 0.25 h⁻¹ Room Temperature tryptone 4 LB, 0.5 g/L bacto-0.31 hr⁻¹ Room Temperature tryptone 5 LB, 3 g/L bacto- 0.38 hr⁻¹ RoomTemperature tryptone 6 LB, 0.5 g/L bacto- 0.38 hr⁻¹ Room Temperaturetryptone

FIGS. 4A-B show growth curves as a function of time in various growthmedia. The red data (5,6,7) represent different concentrations ofbacto-tryptone in LB at a fixed dilution rate whereas the empty circles(3,4,6) depict constant influent nutrient composition at variousdilution rates. FIG. 5 shows Tau I and a function of dilution rates.FIG. 6 shows steady state cell concentrations as a function of dilutionrates in various growth media. Upon inoculation, each chemostat culturebegan with a variable lag period, which depended on the age and size ofthe inoculum. This was replaced by an exponential phase that gave way toa steady-state regime. Steady-state operation was ascertained to bepossible over a range of dilution rates (0.072-0.352 hr⁻¹). Over thisrange, the culture was self-adjusting in that on setting the flow rateto a give value, the concentration of organisms achieved a steady-state.On changing the flow-rate, new steady-states were automaticallyattained.

From observations and measurements made in the experiments, two modelswere constructed of the dynamics in the microfluidic chemostat. Themodels use a small number of parameters to represent the factorsinvolved in controlling cell growth. These models were consistent withthe observations and measurements done in the investigation. The modelsindicate that steady-state nutrient concentration is not in the limitingregime. As such, the steady state observed may be due to something otherthan nutrient depletion. The steady state may therefore be attributed totoxic metabolite accumulation, or a quorum sensing dependent mechanism.

First Model for Bacterial Growth

To probe the dynamics of bacterial growth in the chemostat system usedin the experiments, we modified the conventional chemostat model toaccount for previous observation that the growth rate of E. colicultures is also regulated by the detection and quantitative analysis ofthe cell concentration. We kept the Monod model, which defines therelationship between the specific growth rate and substrateconcentration. We included a term representing cell density-dependentregulation of the growth rate (toxic metabolite or quorum-sensingmolecule accumulation). Thus, microbial growth in the microfluidicchemostat is represented in this model as:

$\begin{matrix}{{\overset{.}{x}}_{1} = {{\mu_{\max}\frac{x_{1}x_{2}}{k_{s} + x_{2}}} - {Dx}_{1} - {\gamma \; x_{1}x_{3}}}} & {{Eq}.\mspace{14mu} 1} \\{{\overset{.}{x}}_{2} = {{D\left( {{aA}^{\prime} - x_{2}} \right)} - {\Lambda \frac{x_{1}x_{2}}{k_{s} + x_{2}}}}} & {{Eq}.\mspace{14mu} 2} \\{{\overset{.}{x}}_{3} = {{\xi \; x_{1}} - {Dx}_{3}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

Here, x₁ is the bacterial population, x₂ the nutrient concentration andx₃ the cell density dependent (CDD) growth inhibitory factor(concentration of toxic metabolites or QS molecules). The first equationexpresses, respectively, bacterial growth by nutrient consumption,dilution at a rate D, and growth-inhibition due to the CDD factor. Thesecond equation describes nutrient injection, dilution, and consumption.The third equation conveys CDD factor production and dilution. μ_(max)is the maximum growth rate that occurs at saturation levels of thegrowth-limiting substrate. D is the dilution rate and k_(s) is thesubstrate concentration, at which growth occurs at half its maximumvalue, ½μ_(max). a is the concentration of the growth-limiting substratein the influent. γ and ξ represent the growth-inhibitory effect of theCDD factor on the microbes and its rate of production by the microbes. Λis the ratio of the growth constant to the yield coefficient.

We simplify this model by assuming that the CDD factor concentration isquasi-steady. Including CDD factor dynamics allows for cellconcentration ‘overshoot’ and oscillate. We ignore that here, and assumesimply:

$\begin{matrix}{x_{3} = {\frac{\xi}{D}x_{1}}} & {{Eq}.\mspace{14mu} 4}\end{matrix}$

We also rescale the two concentration and time variables to reduce thesix-dimensional parameter space by three dimensions. With the followingscalings: t=T/μ_(max), x₁=y₁/Λ, and x₂=k_(s)y₂, the equation set (Eqs.1, 2 and 3) reduces to:

$\begin{matrix}{{\overset{.}{y}}_{1} = {\frac{y_{1}y_{2}}{1 + y_{2}} - {\overset{\_}{D}y_{1}} - {\frac{\Psi}{\overset{\_}{D}}y_{1}^{2}}}} & {{Eq}.\mspace{14mu} 5} \\{{{\overset{.}{y}}_{2} = {{\overset{\_}{D}\left( {{aA} - y_{2}} \right)} - \frac{y_{1}y_{2}}{1 + y_{2}}}}{{where},}} & {{Eq}.\mspace{14mu} 6} \\{{{\overset{\_}{D} = \frac{D}{\mu_{\max}}},{A = \frac{A^{\prime}}{ks}},{and}}{\Psi = \frac{\gamma^{\xi}}{\mu_{\max}\Lambda}}} & \;\end{matrix}$

are the independent parameters governing the dynamics of the system.Here, D is the dilution rate scaled by μ_(max), A is the percentageconcentration of bacto-Tryptone in the influent with respect to theoptimum concentration of 100 gL⁻¹, and Ψ is the ratio of the CDD factorto the initial growth rate. These scalings are chosen because a and Dare the ‘knobs’ that can be turned experimentally. This model allowsbacteria to adjust their growth rate to declining albeit non-limitingnutrient amounts.

Discretized Dilutions:

Dilution in the microfluidic chemostat is performed in discrete steps toaccommodate a sequential lysis scheme. Even with about a 1/15^(th)dilution fraction, the microfluidic discretized-flow culture will reachsteady state. This is observed by analyzing the recursive counterpartsof Eqs. 1, 2 and 3, which govern microbial growth in a discretized-flowsystem.

$\begin{matrix}{{\overset{.}{x}}_{1_{n\; \Delta \; t}} = {{\mu_{\max}\frac{x_{1_{n\; \Delta \; t}}x_{2_{n\; \Delta \; t}}}{k_{s} + x_{2_{n\; \Delta \; t}}}x_{1_{n\; \Delta \; t}}} - {H_{n\; \Delta \; t}\frac{T}{\Delta \; t}{Dx}_{1}} - {\gamma \; x_{1_{n\; \Delta \; t}}x_{3_{n\; \Delta \; t}}}}} & {{Eq}.\mspace{14mu} 8} \\{{\overset{.}{x}}_{2n\; \Delta \; t} = {{H_{n\; \Delta \; t}\frac{T}{\Delta \; t}{D\left( {{aA}^{\prime} - x_{2_{n\; \Delta \; t}}} \right)}} - {\Lambda \frac{x_{1_{n\; \Delta \; t}}x_{2_{n\; \Delta \; t}}}{k_{s} + x_{2_{n\; \Delta \; t}}}}}} & {{Eq}.\mspace{14mu} 9} \\{{\overset{.}{x}}_{3_{n\; \Delta \; t}} = {{\gamma \; x_{1_{n\; \Delta \; t}}} + {H_{n\; \Delta \; t}\frac{T}{\Delta \; t}{Dx}_{3_{n\; \Delta \; t}}}}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$

with initial conditions,

x _(1(n=1)Δt) =x ₁ ⁰ ,x _(2(n=1)Δt) =a,x _(3(n=1)Δt)=0, n=1,2,3 . . .

Here, Δt is the discretized time increment of the simulation and T isthe period between consecutive dilutions. TD is the fraction of thechemostat growth chamber replaced during each dilution. H_(nΔt)represents a Heaviside unit step function defined such that H_(nΔt)=1 ifn is step during which a dilution occurs (the first time unit during thedilution period T) and zero otherwise. At a fixed dilution rate, as thedilution fraction approaches zero, the dilution period T approaches thetime increment Δt. Evidently, the flow becomes continuous and theequation set (Eqs. 8, 9 and 10) becomes identical to set (Eqs. 1, 2 and3).

E. Coli Growth in the Microfluidic Chemostat:

In standard chemostat operation, the influent composition is such thatall the ingredients are in optimal amounts, except for thegrowth-limiting factor, whose concentration is kept sufficiently low. Assuch, the growth-limiting factor determines the growth rate andsteady-state chemostat concentration. In the microfluidic chemostatexperiments, undefined Luria-Bertani (LB) medium was used with variousconcentrations of the bacto-tryptone ingredient. In such complexsubstrate medium, growth at the expense of the substrate utilized at thehighest efficiency leads to the establishment of steady-state,accompanied by an incomplete utilization of the other substratespresent. For this reason, a specific albeit unknown bacto-tryptonecomponent in the influent played the role of growth-limiting factor.

A series of experiments were performed at room temperature (21° C.) withdifferent influent bacto-tryptone concentrations (3 gL⁻¹, 0.5 gL⁻¹, and0.1 gL⁻¹) in micro-chemostats inoculated with about 5 bacteria per μL.In tandem with theory, each of the chemostat cultures began with avariable lag period, which depended on the age and size of the inoculum.This was replaced by an exponential phase that gave way to an indefinitesteady-state regime (see FIGS. 4A-B). Steady-state operation wasascertained to be possible over a range of dilution rates (0.072-0.352hr⁻¹). Over this range, the culture was self-adjusting in that onsetting the flow rate to a given value the concentration of organismswould move towards and settle down at steady-state levels, which aremaintained indefinitely as long as the flow rate is unaltered. Onchanging the flow-rate, new steady-state levels were automaticallyattained.

During the early stage of the exponential growth phase, where thepopulation size is small and the nutrients are non-limiting, thespecific growth rate μ_(max) is given by the equation

$\begin{matrix}{\mu_{\max} \approx {\frac{\left( {\log_{e}x_{1}} \right)}{t} + D}} & {{Eq}.\mspace{14mu} 11}\end{matrix}$

The value d(log_(e)x₁)/dt was determined experimentally by fitting thecell population density x₁(t) to an exponential function of the formy=ae^(bt)+C. The results are displayed in FIGS. 5A-B.

Solving the scaled model for steady-state concentrations gives fourfixed points. One is the trivial fixed point with no bacteria (y₁^(a)=0). Of the other three non-trivial fixed points, only one hadnon-negative cell and nutrient concentrations. The measured initialgrowth rate, μ_(max)≈0.52 hr⁻¹ is constant irrespective of the influentnutrient composition, which is in agreement with the Monod model.

The Steady-State Cell Concentration:

y₁ was scaled with 1/Λ, a parameter which we can not measure. Therefore,all measured cell concentrations were normalized by the value at (a=30%and D=0.47), and y₁ values by y₁(a=30, D=0.47). Reasonable fits areobtained for A=5 and Ψ>0.5 (see FIG. 6). Scaling of y₁ was scaled with1/Λ, a parameter which we can not measure denies us a tight fit for Ψ.Nevertheless, cell density dependent growth inhibition is necessary toexplain the data. To demonstrate this, we carried out a similar analysisfor a system without cell density dependent growth regulation (Ψ=0).This yields steady-state cell and nutrient concentrations:

$\begin{matrix}{{y_{1}^{ss} = {{Aa} - \frac{\overset{\_}{D}}{1 - \overset{\_}{D}}}}{and}{y_{2}^{ss} = \frac{\overset{\_}{D}}{1 - \overset{\_}{D}}}} & {{Eq}.\mspace{14mu} 12}\end{matrix}$

implying that at all dilution rates, steady-state populations will beseparated by a constant proportional to the nutrient concentration,which is not observed experimentally (see FIGS. 4A-B) This shows that Ψis ‘sufficiently large’, which is strong evidence for cell densitydependent growth limitation.

Time Constant for Approaching Steady-State:

Experimental values for the time constant for approaching steady-statewere determined from the chemostat growth curves. Reasonable fits areobtained for A=5 and Ψ>0.5 (see FIG. 7). As such, cell density dependentgrowth limitation is necessary to explain the data. We analyzed thisparameter for a system with Ψ=0. With this condition, time constants toapproach steady state vary like ( D, aA− D−2aA D+ D ²+aA D ²), whichresults in unconvincing fits. This yields time constants.

The model was consistent with the experimental observations andmeasurements. It provided estimates of non-measurable variables such asthe nutrient concentration. Using the fixed-point values for celldensity, the model predicted the steady-state nutrient concentrations.The steady-state nutrient concentrations were found to be in thenon-limiting regime (see FIG. 7). The simple model described aboveproved to be consistent with the experimental measurement (thesteady-state nutrient concentration and time constant for arrival tosteady state).

Second Model for Bacterial Growth

A second model was also used to describe microbial growth in thechemostat. This second model combines the Monod model defining therelationship between the specific growth rate and substrateconcentration for substrate-limited growth and a model developed by C.C. Spicer to describe the rate nutrient consumption and growthlimitation by toxic metabolites. In the second model, the differentialequations used to describe microbial growth in the chemostat at adilution rate D are:

$\begin{matrix}{{\frac{1}{x_{1}}\frac{x_{1}}{t}} = {\frac{\mu_{\max}x_{2}}{k_{s} + x_{2}} - D - {\zeta \; x_{3}}}} & {{Eq}.\mspace{14mu} 13} \\{\frac{x_{2}}{t} = {{D\left( {a - x_{2}} \right)} - {\frac{1}{Y_{x_{1}/x_{2}}}\left( \frac{\mu_{\max}x_{2}}{x_{2} + k_{s}} \right)x_{1}}}} & {{Eq}.\mspace{14mu} 14} \\{\frac{x_{3}}{t} = {{\gamma \; x_{1}} - {Dx}_{3}}} & {{Eq}.\mspace{14mu} 15}\end{matrix}$

Here, x₁, x₂ and x₃ represent the microbial population size,growth-limiting nutrient concentration and toxic metaboliteconcentration, respectively. μ_(max) is the growth rate constant (i.e.the maximum growth rate that occur at saturation levels of thegrowth-limiting factor) and k_(s) is the substrate concentration atwhich growth occurs at half its maximum value, ½μ_(max). a is theconcentration of the growth-limiting substrate in the influent. Theconstants ζ and γ represent the lethal effect of the toxic metabolite onthe microbes and its rate of production by them. Y_(x1/x2) is the yieldcoefficient, representing the weight of bacteria formed per amount ofgrowth-limiting substrate consumed.

During the initial stage of the exponential growth phase when the celldensity is low, the toxic metabolite concentration x₃ is negligiblysmall. Under these conditions, the growth-limiting substrateconcentration is high compared to k_(s). As such, Eq. 13 reduces to:

$\begin{matrix}{{\frac{1}{x_{1}}\frac{x_{1}}{t}} = {{\left. \frac{\left( {\log_{e}x_{1}} \right)}{t} \right.\sim\mu_{\max}} - D}} & {{Eq}.\mspace{14mu} 16}\end{matrix}$

During steady-state, the concentration of the growth-limiting substrateis quite small. Under such conditions, the microbial growth rate islinearly proportional to the concentration of the growth-limitingfactor. As such the growth governing differential equations at steadystate reduce to:

$\begin{matrix}{{\frac{1}{x_{1}}\frac{x_{1}}{t}} = {{{\lambda \; x_{2}} - D - {\zeta \; x_{3}}} = 0}} & {{Eq}.\mspace{14mu} 17} \\{\frac{x_{2}}{t} = {{{D\left( {a - x_{2}} \right)} - {\kappa \; x_{1}x_{2}}} = 0}} & {{Eq}.\mspace{14mu} 18} \\{\frac{x_{3}}{t} = {{{\gamma \; x_{1}} - {Dx}_{3}} = 0}} & {{Eq}.\mspace{14mu} 19}\end{matrix}$

where λ is the constant of proportionality relating the growth rate tothe growth-limiting nutrient concentration and κ is the rate ofconsumption of growth-limiting nutrient per bacteria. As such, λ/κ isthe amount of growth factor required to create a single organism.

At high dilution rates, the cell density the steady-state cell densityis suppressed. For this reason, we can estimate the value of κ byneglecting the concentration as well as effect of the toxic metabolites.The steady-state nutrient concentration ({tilde over (x)}₂), and theconstant κ can be determined from Eq. 17 and Eq. 18, respectively, as:

$\begin{matrix}{\kappa = {\frac{1}{x_{1}}\left( {{\lambda \; a} - D_{high}} \right)}} & {{Eq}.\mspace{14mu} 20}\end{matrix}$

When the dilution rate is lowered, the steady-state cell densityincreases, and the toxic metabolite concentration becomes significant.From Eq. 18 and 19 we determine {tilde over (x)}₂ and {tilde over (x)}₃(in terms of γ):

$\begin{matrix}{{\overset{\sim}{x}}_{2} = \frac{D_{low}a}{D_{low} + {\kappa \; {\overset{\sim}{x}}_{1}}}} & {{Eq}.\mspace{14mu} 21} \\{{\overset{\sim}{x}}_{3} = {\frac{\gamma}{D_{low}}{\overset{\sim}{x}}_{1}}} & {{Eq}.\mspace{14mu} 22}\end{matrix}$

For mathematical convenience γ is reserved as a bookkeeping parameterfor unit conversion purposes in Eq. 13 and its value is confined tounity. The constant μ thus becomes:

$\begin{matrix}{\mu = {\frac{1}{\gamma}\left\lfloor {\frac{D_{low}}{\lambda}\left( {{\lambda \; {\overset{\sim}{x}}_{2}} - D_{low}} \right)} \right\rfloor}} & {{Eq}.\mspace{14mu} 23}\end{matrix}$

Discretized Dilutions:

The chemostat system used in the experiments are operated a discretemode (i.e., non-continuous). Dilutions are performed in discrete stepsto prohibit the exposure of all the cells in the growth chamber to thelysis buffer. The model is also premised on each discrete dilution stepdecreasing the microbial population by a sixteenth. Even with such adilution fraction, a microfluidic microbial discretized-flow system willreach steady state. The discretized and continuous modes of operationcan be reconciled by analyzing the set of recursive equations thatgovern microbial growth in a discretized-flow system.

$\begin{matrix}{x_{1_{n\; \Delta \; t}} = {x_{1_{{({n - 1})}\Delta \; t}} + {\left\lfloor \frac{x_{1}}{t} \right\rfloor_{{({n - 1})}\Delta \; t}\Delta \; t}}} & {{Eq}.\mspace{14mu} 24} \\{x_{2_{n\; \Delta \; t}} = {x_{2_{{({n - 1})}\Delta \; t}} + {\left\lfloor \frac{x_{2}}{t} \right\rfloor_{{({n - 1})}\Delta \; t}\Delta \; t}}} & {{Eq}.\mspace{14mu} 25} \\{x_{3_{n\; \Delta \; t}} = {x_{31_{{({n - 1})}\Delta \; t}} + {\left\lfloor \frac{x_{31}}{t} \right\rfloor_{{({n - 1})}\Delta \; t}\Delta \; t}}} & {{Eq}.\mspace{14mu} 26} \\{\left\lfloor \frac{x_{1}}{t} \right\rfloor_{n\; \Delta \; t} = {{x_{1_{n\; \Delta \; t}}\left\lbrack {{\lambda \; x_{2_{n\; \Delta \; t}}} - {\mu \; x_{3_{n\; \Delta \; t}}}} \right\rbrack} - {\frac{1}{\Delta \; t}{H(t)}{Fx}_{1_{n\; \Delta \; t}}}}} & {{Eq}.\mspace{14mu} 27} \\{\left\lfloor \frac{x_{2}}{t} \right\rfloor_{n\; \Delta \; t} = {{\kappa \; x_{1_{n\; \Delta \; t}}x_{2_{n\; \Delta \; t}}} + {\frac{1}{\Delta \; t}{H(t)}{F\left\lbrack {a - x_{2_{n\; \Delta \; t}}} \right\rbrack}}}} & {{Eq}.\mspace{14mu} 28} \\{{\left\lfloor \frac{x_{3}}{t} \right\rfloor_{n\; \Delta \; t}\gamma \; x_{1_{n\; \Delta \; t}}} + {\frac{1}{\Delta \; t}{H(t)}x_{3_{n\; \Delta \; t}}}} & {{Eq}.\mspace{14mu} 29} \\{x_{1{({n = 0})}\Delta \; t} = x_{1_{0}}} & {{Eq}.\mspace{14mu} 30} \\{x_{2{({n = 0})}\Delta \; t} = a} & {{Eq}.\mspace{14mu} 31} \\{x_{3{({n = 0})}\Delta \; t} = x_{3_{0}}} & {{Eq}.\mspace{14mu} 32}\end{matrix}$

Where Δt is the discretized time increment of the simulation, F is thefraction of the chemostat replaced during each dilution, H(t) is aHeaviside unit step function defined such that H(t)=1 at the beginningof a dilution and H(t)=0 otherwise. The dilution rate D is replaced bythe fact that dilutions are performed periodically according to a timeperiod T=F/D. At a fixed dilution rate, as the dilution fractionapproaches zero, the dilution period shrinks, and the flow becomescontinuous.

Growth in Continuous Culture:

In standard chemostat operation, the influent contains optimumconcentrations of all growth factors required by the bacterium, with theexception of one, the growth-limiting factor. The growth-limitingfactor, whose concentration is kept relatively low, determines the celldensity in the resident culture during steady-state. In the microfluidicchemostat experiments, undefined Luria-Bertani (LB) medium was used withvarious concentrations of the bacto-tryptone ingredient. In such complexsubstrate medium, growth at the expense of the substrate utilized at thehighest efficiency leads to the establishment of steady-state,accompanied by and incomplete utilization of the other substratespresent. For this reason, a specific albeit unknown bacto-tryptonecomponent in the influent served as the growth-limiting factor.

During the early stage of the exponential growth phase, when the celldensity is low, the toxic metabolite concentration is negligibly small.Under these conditions, the organisms are growing in substrateconcentrations, which are high compared to κ_(s), implying that thespecific growth rate is approximately equal to μ_(max). As such, thespecific growth rate of the E. Coli strain was determined at variousdilution rates using the microfluidic apparatus under the experimentalconditions according to the equation:

$\begin{matrix}{\mu_{\max} \approx {\frac{\left( {\log_{e}x} \right)}{t} + D}} & {{Eq}.\mspace{14mu} 33}\end{matrix}$

The value d(log_(e) x)/dt was determined from the constant, b, obtainedby fitting X_(l)(t) to an exponential function of the form y=ae^(bt)+c.Typical experimental results are shown in FIG. 4.

Experiments were performed at room temperature (21° C.) with differentinitial bacto-tryptone concentrations in chemostats inoculated withabout 5 bacteria per μL. In tandem with theory, each of the chemostatcultures began with a variable lag period, which depended on the age andsize of the inoculum. This was replaced by an exponential phase thatgave way to an indefinite steady-state regime. Steady-state operationwas ascertained to be possible over a range of dilution rates (0.2. to0.4). Over this rate of dilution rates, the culture was self-adjustingin that on setting the flow rate to a given value, the concentration oforganisms would move towards and settle down at steady-state levelswhich are maintained indefinitely as long as the flow rate is unaltered;on changing the flow-rate, new steady-state levels were automaticallyattained.

Effect of Influent Substrate Concentration:

At high dilution rates, the steady-state concentration is proportionalto the bacto-tryptone concentration in the influent. However, thisproportionality fades away as the dilution rate is lowered. Thisphenomenon could be attributed to growth limitation by the microbialtoxic metabolites. At high dilution rates, which favor low steady-statecell densities, the concentration as well as the effect of the toxicmetabolites is restrained. As the dilution rate is lowered, the cellculture self-adjusts in an attempt to arrive and settle at a highersteady-state cell concentration. In tandem with the cell density, thetoxic metabolite concentration increases to growth-limiting levels. Assuch, at a fixed dilution rate, different bacto-tryptone concentrationsin the influent result in the same cell density.

In FIG. 16 the three graphs show the E. coli cell density in the microfluidic chemostat as a function of time at different influentbacto-tryptone concentrations at room temperature and a fixed dilutionrate D=0.377 hr⁻¹. We were also able to control the growth rate of thebacteria by adjusting the dilution rates.

LB is a complex medium with several carbon sources that might beexpected to engender complex chemostat dynamics. In such a medium,growth fueled by the substrate utilized at the highest initialefficiency can lead to the establishment of a transient steady-state,accompanied by conversion of bacterial metabolism to utilization ofother substrates. Surprisingly, the chemostat was observed to achievesimple steady state growth with a population whose absolute value variedwith the concentration of bacto-tryptone. As expected from the Monodmodel, the initial growth constants immediately after inoculation wereindependent of nutrient concentration and dilution rate, and representthe intrinsic growth rates of the bacteria. Approaching steady state,the bacteria appear to “lock on” to the dilution rate while becomingnutrient limited, and their growth rates were observed to slow down. Thesteady state concentrations in the reactor scale with dilution rate andgrowth-limiting factor in a manner consistent with the simple Monodmodel.

Discussion of Formation of Microfabricated Fluidic Devices I.Microfabircation Overview

The following discussion relates to formation of microfabricated fluidicdevices utilizing elastomer materials, as described generally incommonly assigned U.S. patent application Ser. No. 09/826,585 filed Apr.6, 2001, Ser, No. 09/724,784 filed Nov. 28, 2000, and Ser. No.09/605,520, filed Jun. 27, 2000. These patent applications are herebyincorporated by reference in their entirety for all purposes. Additionaldetails may also be found in U.S. Pat. No. 6,408,878 to Unger et al,issued Jun. 25, 2002, the entire contents of which is also herebyincorporated by reference in its entirety for all purposes.

1. Methods of Fabricating

Exemplary methods of fabricating the present invention are providedherein. It is to be understood that the present invention is not limitedto fabrication by one or the other of these methods. Rather, othersuitable methods of fabricating the present microstructures, includingmodifying the present methods, are also contemplated.

FIGS. 7 to 14B illustrate sequential steps of a first preferred methodof fabricating the present microstructure, (which may be used as a pumpor valve). FIGS. 15 to 25 illustrate sequential steps of a secondpreferred method of fabricating the present microstructure, (which alsomay be used as a pump or valve).

As will be explained, the preferred method of FIGS. 8 to 15B involvesusing pre-cured elastomer layers which are assembled and bonded. In analternative method, each layer of elastomer may be cured “in place”. Inthe following description “channel” refers to a recess in theelastomeric structure which can contain a flow of fluid or gas.

Referring to FIG. 8, a first micro-machined mold 10 is provided.Micromachined mold 10 may be fabricated by a number of conventionalsilicon processing methods, including but not limited tophotolithography, ion-milling, and electron beam lithography.

As can be seen, micro-machined mold 10 has a raised line or protrusion11 extending therealong. A first elastomeric layer 20 is cast on top ofmold 10 such that a first recess 21 will be formed in the bottom surfaceof elastomeric layer 20, (recess 21 corresponding in dimension toprotrusion 11), as shown.

As can be seen in FIG. 9, a second micro-machined mold 12 having araised protrusion 13 extending therealong is also provided. A secondelastomeric layer 22 is cast on top of mold 12, as shown, such that arecess 23 will be formed in its bottom surface corresponding to thedimensions of protrusion 13.

As can be seen in the sequential steps illustrated in FIGS. 10 and 21,second elastomeric layer 22 is then removed from mold 12 and placed ontop of first elastomeric layer 20. As can be seen, recess 23 extendingalong the bottom surface of second elastomeric layer 22 will form a flowchannel 32.

Referring to FIG. 12, the separate first and second elastomeric layers20 and 22 (FIG. 4) are then bonded together to form an integrated (i.e.:monolithic) elastomeric structure 24.

As can been seen in the sequential step of FIGS. 13 and 14A, elastomericstructure 24 is then removed from mold 10 and positioned on top of aplanar substrate 14. As can be seen in FIGS. 14A and 14B, whenelastomeric structure 24 has been sealed at its bottom surface to planarsubstrate 14, recess 21 will form a flow channel 30.

The present elastomeric structures form a reversible hermetic seal withnearly any smooth planar substrate. An advantage to forming a seal thisway is that the elastomeric structures may be peeled up, washed, andre-used. In preferred aspects, planar substrate 14 is glass. A furtheradvantage of using glass is that glass is transparent, allowing opticalinterrogation of elastomer channels and reservoirs. Alternatively, theelastomeric structure may be bonded onto a flat elastomer layer by thesame method as described above, forming a permanent and high-strengthbond. This may prove advantageous when higher back pressures are used.

As can be seen in FIGS. 14A and 14B, flow channels 30 and 32 arepreferably disposed at an angle to one another with a small membrane 25of substrate 24 separating the top of flow channel 30 from the bottom offlow channel 32.

In preferred aspects, planar substrate 14 is glass. An advantage ofusing glass is that the present elastomeric structures may be peeled up,washed and reused. A further advantage of using glass is that opticalsensing may be employed. Alternatively, planar substrate 14 may be anelastomer itself, which may prove advantageous when higher backpressures are used.

The method of fabrication just described may be varied to form astructure having a membrane composed of an elastomeric materialdifferent than that forming the walls of the channels of the device.This variant fabrication method is illustrated in FIGS. 14C-14G.

Referring to FIG. 14C, a first micro-machined mold 10 is provided.Micromachined mold 10 has a raised line or protrusion 11 extendingtherealong. In FIG. 14D, first elastomeric layer 20 is cast on top offirst micro-machined mold 10 such that the top of the first elastomericlayer 20 is flush with the top of raised line or protrusion 11. This maybe accomplished by carefully controlling the volume of elastomericmaterial spun onto mold 10 relative to the known height of raised line11. Alternatively, the desired shape could be formed by injectionmolding.

In FIG. 14E, second micro-machined mold 12 having a raised protrusion 13extending therealong is also provided. Second elastomeric layer 22 iscast on top of second mold 12 as shown, such that recess 23 is formed inits bottom surface corresponding to the dimensions of protrusion 13.

In FIG. 14F, second elastomeric layer 22 is removed from mold 12 andplaced on top of third elastomeric layer 222. Second elastomeric layer22 is bonded to third elastomeric layer 20 to form integral elastomericblock 224 using techniques described in detail below. At this point inthe process, recess 23 formerly occupied by raised line 13 will formflow channel 23.

In FIG. 14G, elastomeric block 224 is placed on top of firstmicro-machined mold 10 and first elastomeric layer 20. Elastomeric blockand first elastomeric layer 20 are then bonded together to form anintegrated (i.e., monolithic) elastomeric structure 24 having a membranecomposed of a separate elastomeric layer 222.

When elastomeric structure 24 has been sealed at its bottom surface to aplanar substrate in the manner described above in connection with FIG.14A, the recess formerly occupied by raised line 11 will form flowchannel 30.

The variant fabrication method illustrated above in conjunction withFIGS. 14C-14G offers the advantage of permitting the membrane portion tobe composed of a separate material than the elastomeric material of theremainder of the structure. This is important because the thickness andelastic properties of the membrane play a key role in operation of thedevice. Moreover, this method allows the separate elastomer layer toreadily be subjected to conditioning prior to incorporation into theelastomer structure. As discussed in detail below, examples ofpotentially desirable condition include the introduction of magnetic orelectrically conducting species to permit actuation of the membrane,and/or the introduction of dopant into the membrane in order to alterits elasticity.

While the above method is illustrated in connection with forming variousshaped elastomeric layers formed by replication molding on top of amicromachined mold, the present invention is not limited to thistechnique. Other techniques could be employed to form the individuallayers of shaped elastomeric material that are to be bonded together.For example, a shaped layer of elastomeric material could be formed bylaser cutting or injection molding, or by methods utilizing chemicaletching and/or sacrificial materials as discussed below in conjunctionwith the second exemplary method.

An alternative method fabricates a patterned elastomer structureutilizing development of photoresist encapsulated within elastomermaterial. However, the methods in accordance with the present inventionare not limited to utilizing photoresist. Other materials such as metalscould also serve as sacrificial materials to be removed selective to thesurrounding elastomer material, and the method would remain within thescope of the present invention. For example, gold metal may be etchedselective to RTV 615 elastomer utilizing the appropriate chemicalmixture.

2. Layer and Channel Dimensions

Microfabricated refers to the size of features of an elastomericstructure fabricated in accordance with an embodiment of the presentinvention. In general, variation in at least one dimension ofmicrofabricated structures is controlled to the micron level, with atleast one dimension being microscopic (i.e. below 1000 μm).Microfabrication typically involves semiconductor or MEMS fabricationtechniques such as photolithography and spincoating that are designedfor to produce feature dimensions on the microscopic level, with atleast some of the dimension of the microfabricated structure requiring amicroscope to reasonably resolve/image the structure.

In preferred aspects, flow channels 30, 32, 60 and 62 preferably havewidth-to-depth ratios of about 10:1. A non-exclusive list of otherranges of width-to-depth ratios in accordance with embodiments of thepresent invention is 0.1:1 to 100:1, more preferably 1:1 to 50:1, morepreferably 2:1 to 20:1, and most preferably 3:1 to 15:1. In an exemplaryaspect, flow channels 30, 32, 60 and 62 have widths of about 1 to 1000microns. A non-exclusive list of other ranges of widths of flow channelsin accordance with embodiments of the present invention is 0.01 to 1000microns, more preferably 0.05 to 1000 microns, more preferably 0.2 to500 microns, more preferably 1 to 250 microns, and most preferably 10 to200 microns. Exemplary channel widths include 0.1 μm, 1 μm, 2 μm, 5 μm,10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm,110 μm, 120 μm, 130 μm, 140 μm, 150 μm, 160 μm, 170 μm, 180 μm, 190 μm,200 μm, 210 μm, 220 μm, 230 μm, 240 μm, and 250 μm.

Flow channels 30, 32, 60, and 62 have depths of about 1 to 100 microns.A non-exclusive list of other ranges of depths of flow channels inaccordance with embodiments of the present invention is 0.01 to 1000microns, more preferably 0.05 to 500 microns, more preferably 0.2 to 250microns, and more preferably 1 to 100 microns, more preferably 2 to 20microns, and most preferably 5 to 10 microns. Exemplary channel depthsinclude including 0.01 μm, 0.02 μm, 0.05 μm, 0.1 μm, 0.2 μm, 0.5 μm, 1μm, 2 μm, 3 μm, 4 μm, 5 μm, 7.5 μm, 10 μm, 12.5 μm, 15 μm, 17.5 μm, 20μm, 22.5 μm, 25 μm, 30 μm, 40 μm, 50 μm, 75 μm, 100 μm, 150 μm, 200 μm,and 250 μm.

The flow channels are not limited to these specific dimension ranges andexamples given above, and may vary in width in order to affect themagnitude of force required to deflect the membrane as discussed atlength below in conjunction with FIG. 34. For example, extremely narrowflow channels having a width on the order of 0.01 m may be useful inoptical and other applications, as discussed in detail below.Elastomeric structures which include portions having channels of evengreater width than described above are also contemplated by the presentinvention, and examples of applications of utilizing such wider flowchannels include fluid reservoir and mixing channel structures.

The Elastomeric layers may be cast thick for mechanical stability. In anexemplary embodiment, elastomeric layer 22 of FIG. 8 is 50 microns toseveral centimeters thick, and more preferably approximately 4 mm thick.A non-exclusive list of ranges of thickness of the elastomer layer inaccordance with other embodiments of the present invention is betweenabout 0.1 micron to 10 cm, 1 micron to 5 cm, 10 microns to 2 cm, 100microns to 10 mm.

Accordingly, membrane 25 of FIG. 14B separating flow channels 30 and 32has a typical thickness of between about 0.01 and 1000 microns, morepreferably 0.05 to 500 microns, more preferably 0.2 to 250, morepreferably 1 to 100 microns, more preferably 2 to 50 microns, and mostpreferably 5 to 40 microns. As such, the thickness of elastomeric layer22 is about 100 times the thickness of elastomeric layer 20. Exemplarymembrane thicknesses include 0.01 μm, 0.02 μm, 0.03 μm, 0.05 μm, 0.1 μm,0.2 μm, 0.3 μm, 0.5 μm, 1 μm, 2 μm, 3 μm, 5 μm, 7.5 μm, 10 μm, 12.5 μm,15 μm, 17.5 μm, 20 μm, 22.5 μm, 25 μm, 30 μm, 40 μm, 50 μm, 75 μm, 100μm, 150 μm, 200 μm, 250 μm, 300 μm, 400 μm, 500 μm, 750 μm, and 1000 μm.

3. Soft Lithographic Bonding

Preferably, elastomeric layers are bonded together chemically, usingchemistry that is intrinsic to the polymers comprising the patternedelastomer layers. Most preferably, the bonding comprises two component“addition cure” bonding.

In a preferred aspect, the various layers of elastomer are boundtogether in a heterogenous bonding in which the layers have a differentchemistry. Alternatively, a homogenous bonding may be used in which alllayers would be of the same chemistry. Thirdly, the respective elastomerlayers may optionally be glued together by an adhesive instead. In afourth aspect, the elastomeric layers may be thermoset elastomers bondedtogether by heating.

In one aspect of homogeneous bonding, the elastomeric layers arecomposed of the same elastomer material, with the same chemical entityin one layer reacting with the same chemical entity in the other layerto bond the layers together. In one embodiment, bonding between polymerchains of like elastomer layers may result from activation of acrosslinking agent due to light, heat, or chemical reaction with aseparate chemical species.

Alternatively in a heterogeneous aspect, the elastomeric layers arecomposed of different elastomeric materials, with a first chemicalentity in one layer reacting with a second chemical entity in anotherlayer. In one exemplary heterogenous aspect, the bonding process used tobind respective elastomeric layers together may comprise bondingtogether two layers of RTV 615 silicone. RTV 615 silicone is a two-partaddition-cure silicone rubber. Part A contains vinyl groups andcatalyst; part B contains silicon hydride (Si—H) groups. Theconventional ratio for RTV 615 is 10A:1B. For bonding, one layer may bemade with 30A:1B (i.e., excess vinyl groups) and the other with 3A:1B(i.e., excess Si—H groups). Each layer is cured separately. When the twolayers are brought into contact and heated at elevated temperature, theybond irreversibly forming a monolithic elastomeric substrate.

In an exemplary aspect of the present invention, elastomeric structuresare formed utilizing Sylgard 182, 184 or 186, or aliphatic urethanediacrylates such as (but not limited to) Ebecryl 270 or Irr 245 from UCBChemical.

In one embodiment in accordance with the present invention, two-layerelastomeric structures were fabricated from pure acrylated Urethane Ebe270. A thin bottom layer was spin coated at 8000 rpm for 15 seconds at170° C. The top and bottom layers were initially cured under ultravioletlight for 10 minutes under nitrogen utilizing a Model ELC 500 devicemanufactured by Electrolite corporation. The assembled layers were thencured for an additional 30 minutes. Reaction was catalyzed by a 0.5%vol/vol mixture of Irgacure 500 manufactured by Ciba-Geigy Chemicals.The resulting elastomeric material exhibited moderate elasticity andadhesion to glass.

In another embodiment in accordance with the present invention,two-layer elastomeric structures were fabricated from a combination of25% Ebe 270/50% Irr245/25% isopropyl alcohol for a thin bottom layer,and pure acrylated Urethane Ebe 270 as a top layer. The thin bottomlayer was initially cured for 5 min, and the top layer initially curedfor 10 minutes, under ultraviolet light under nitrogen utilizing a ModelELC 500 device manufactured by Electrolite corporation. The assembledlayers were then cured for an additional 30 minutes. Reaction wascatalyzed by a 0.5% vol/vol mixture of Irgacure 500 manufactured byCiba-Geigy Chemicals. The resulting elastomeric material exhibitedmoderate elasticity and adhered to glass.

Alternatively, other bonding methods may be used, including activatingthe elastomer surface, for example by plasma exposure, so that theelastomer layers/substrate will bond when placed in contact. Forexample, one possible approach to bonding together elastomer layerscomposed of the same material is set forth by Duffy et al, “RapidPrototyping of Microfluidic Systems in Poly (dimethylsiloxane)”,Analytical Chemistry (1998), 70, 4974-4984, incorporated herein byreference. This paper discusses that exposing polydimethylsiloxane(PDMS) layers to oxygen plasma causes oxidation of the surface, withirreversible bonding occurring when the two oxidized layers are placedinto contact.

Yet another approach to bonding together successive layers of elastomeris to utilize the adhesive properties of uncured elastomer.Specifically, a thin layer of uncured elastomer such as RTV 615 isapplied on top of a first cured elastomeric layer. Next, a second curedelastomeric layer is placed on top of the uncured elastomeric layer. Thethin middle layer of uncured elastomer is then cured to produce amonolithic elastomeric structure. Alternatively, uncured elastomer canbe applied to the bottom of a first cured elastomer layer, with thefirst cured elastomer layer placed on top of a second cured elastomerlayer. Curing the middle thin elastomer layer again results in formationof a monolithic elastomeric structure.

Where encapsulation of sacrificial layers is employed to fabricate theelastomer structure, bonding of successive elastomeric layers may beaccomplished by pouring uncured elastomer over a previously curedelastomeric layer and any sacrificial material patterned thereupon.Bonding between elastomer layers occurs due to interpenetration andreaction of the polymer chains of an uncured elastomer layer with thepolymer chains of a cured elastomer layer. Subsequent curing of theelastomeric layer will create a bond between the elastomeric layers andcreate a monolithic elastomeric structure.

Referring to the first method of FIGS. 8 to 15B, first elastomeric layer20 may be created by spin-coating an RTV mixture on microfabricated mold12 at 2000 rpm's for 30 seconds yielding a thickness of approximately 40microns. Second elastomeric layer 22 may be created by spin-coating anRTV mixture on microfabricated mold 11. Both layers 20 and 22 may beseparately baked or cured at about 80° C. for 1.5 hours. The secondelastomeric layer 22 may be bonded onto first elastomeric layer 20 atabout 80° C. for about 1.5 hours.

Micromachined molds 10 and 12 may be patterned photoresist on siliconwafers. In an exemplary aspect, a Shipley SJR 5740 photoresist was spunat 2000 rpm patterned with a high resolution transparency film as a maskand then developed yielding an inverse channel of approximately 10microns in height. When baked at approximately 200° C. for about 30minutes, the photoresist reflows and the inverse channels becomerounded. In preferred aspects, the molds may be treated withtrimethylchlorosilane (TMCS) vapor for about a minute before each use inorder to prevent adhesion of silicone rubber.

4. Suitable Elastomeric Materials

Allcock et al, Contemporary Polymer Chemistry, 2nd Ed. describeselastomers in general as polymers existing at a temperature betweentheir glass transition temperature and liquefaction temperature.Elastomeric materials exhibit elastic properties because the polymerchains readily undergo torsional motion to permit uncoiling of thebackbone chains in response to a force, with the backbone chainsrecoiling to assume the prior shape in the absence of the force. Ingeneral, elastomers deform when force is applied, but then return totheir original shape when the force is removed. The elasticity exhibitedby elastomeric materials may be characterized by a Young's modulus.Elastomeric materials having a Young's modulus of between about 1 Pa-1TPa, more preferably between about 10 Pa-100 GPa, more preferablybetween about 20 Pa-1 GPa, more preferably between about 50 Pa-10 MPa,and more preferably between about 100 Pa-1 MPa are useful in accordancewith the present invention, although elastomeric materials having aYoung's modulus outside of these ranges could also be utilized dependingupon the needs of a particular application.

The systems of the present invention may be fabricated from a widevariety of elastomers. In an exemplary aspect, the elastomeric layersmay preferably be fabricated from silicone rubber. However, othersuitable elastomers may also be used.

In an exemplary aspect of the present invention, the present systems arefabricated from an elastomeric polymer such as GE RTV 615 (formulation),a vinylsilane crosslinked (type) silicone elastomer (family). However,the present systems are not limited to this one formulation, type oreven this family of polymer; rather, nearly any elastomeric polymer issuitable. An important requirement for the preferred method offabrication of the present microvalves is the ability to bond multiplelayers of elastomers together. In the case of multilayer softlithography, layers of elastomer are cured separately and then bondedtogether. This scheme requires that cured layers possess sufficientreactivity to bond together. Either the layers may be of the same type,and are capable of bonding to themselves, or they may be of twodifferent types, and are capable of bonding to each other. Otherpossibilities include the use an adhesive between layers and the use ofthermoset elastomers.

Given the tremendous diversity of polymer chemistries, precursors,synthetic methods, reaction conditions, and potential additives, thereare a huge number of possible elastomer systems that could be used tomake monolithic elastomeric microvalves and pumps. Variations in thematerials used will most likely be driven by the need for particularmaterial properties, i.e. solvent resistance, stiffness, gaspermeability, or temperature stability.

There are many, many types of elastomeric polymers. A brief descriptionof the most common classes of elastomers is presented here, with theintent of showing that even with relatively “standard” polymers, manypossibilities for bonding exist. Common elastomeric polymers includepolyisoprene, polybutadiene, polychloroprene, polyisobutylene,poly(styrene-butadiene-styrene), the polyurethanes, and silicones.

Polyisoprene, Polybutadiene, Polychloroprene:

Polyisoprene, polybutadiene, and polychloroprene are all polymerizedfrom diene monomers, and therefore have one double bond per monomer whenpolymerized. This double bond allows the polymers to be converted toelastomers by vulcanization (essentially, sulfur is used to formcrosslinks between the double bonds by heating). This would easily allowhomogeneous multilayer soft lithography by incomplete vulcanization ofthe layers to be bonded; photoresist encapsulation would be possible bya similar mechanism.

Polyisobutylene:

Pure polyisobutylene has no double bonds, but is crosslinked to use asan elastomer by including a small amount (.about.1%) of isoprene in thepolymerization. The isoprene monomers give pendant double bonds on thepolyisobutylene backbone, which may then be vulcanized as above.

Poly(Styrene-Butadiene-Styrene):

Poly(styrene-butadiene-styrene) is produced by living anionicpolymerization (that is, there is no natural chain-terminating step inthe reaction), so “live” polymer ends can exist in the cured polymer.This makes it a natural candidate for the present photoresistencapsulation system (where there will be plenty of unreacted monomer inthe liquid layer poured on top of the cured layer). Incomplete curingwould allow homogeneous multilayer soft lithography (A to A bonding).The chemistry also facilitates making one layer with extra butadiene(“A”) and coupling agent and the other layer (“B”) with a butadienedeficit (for heterogeneous multilayer soft lithography). SBS is a“thermoset elastomer”, meaning that above a certain temperature it meltsand becomes plastic (as opposed to elastic); reducing the temperatureyields the elastomer again. Thus, layers can be bonded together byheating.

Polyurethanes:

Polyurethanes are produced from di-isocyanates (A-A) and di-alcohols ordiamines (B-B); since there are a large variety of di-isocyanates anddialcohols/amines, the number of different types of polyurethanes ishuge. The A vs. B nature of the polymers, however, would make themuseful for heterogeneous multilayer soft lithography just as RTV 615 is:by using excess A-A in one layer and excess B-B in the other layer.

Silicones:

Silicone polymers probably have the greatest structural variety, andalmost certainly have the greatest number of commercially availableformulations. The vinyl-to-(Si—H) crosslinking of RTV 615 (which allowsboth heterogeneous multilayer soft lithography and photoresistencapsulation) has already been discussed, but this is only one ofseveral crosslinking methods used in silicone polymer chemistry.

5. Operation of Device

FIGS. 14B and 14H together show the closing of a first flow channel bypressurizing a second flow channel, with FIG. 14B (a front sectionalview cutting through flow channel 32 in corresponding FIG. 14A), showingan open first flow channel 30; with FIG. 14H showing first flow channel30 closed by pressurization of the second flow channel 32.

Referring to FIG. 14B, first flow channel 30 and second flow channel 32are shown. Membrane 25 separates the flow channels, forming the top offirst flow channel 30 and the bottom of second flow channel 32. As canbe seen, flow channel 30 is “open”.

As can be seen in FIG. 14H, pressurization of flow channel 32 (either bygas or liquid introduced therein) causes membrane 25 to deflectdownward, thereby pinching off flow F passing through flow channel 30.Accordingly, by varying the pressure in channel 32, a linearly actuablevalving system is provided such that flow channel 30 can be opened orclosed by moving membrane 25 as desired. (For illustration purposesonly, channel 30 in FIG. 14G is shown in a “mostly closed” position,rather than a “fully closed” position).

Since such valves are actuated by moving the roof of the channelsthemselves (i.e.: moving membrane 25) valves and pumps produced by thistechnique have a truly zero dead volume, and switching valves made bythis technique have a dead volume approximately equal to the activevolume of the valve, for example about 100×100×10 μm=100 pL. Such deadvolumes and areas consumed by the moving membrane are approximately twoorders of magnitude smaller than known conventional microvalves. Smallerand larger valves and switching valves are contemplated in the presentinvention, and a non-exclusive list of ranges of dead volume includes 1aL to 1 μL, 100 aL to 100 n L, 1 fl to 10 nL, 100 fL to 1 nL, and 1 pLto 100 pL.

The extremely small volumes capable of being delivered by pumps andvalves in accordance with the present invention represent a substantialadvantage. Specifically, the smallest known volumes of fluid capable ofbeing manually metered is around 0.1 μl. The smallest known volumescapable of being metered by automated systems is about ten-times larger(1 μl). Utilizing pumps and valves in accordance with the presentinvention, volumes of liquid of 10 nl or smaller can routinely bemetered and dispensed. The accurate metering of extremely small volumesof fluid enabled by the present invention would be extremely valuable ina large number of biological applications, including diagnostic testsand assays.

Equation 1 represents a highly simplified mathematical model ofdeflection of a rectangular, linear, elastic, isotropic plate of uniformthickness by an applied pressure:

w=(BPb ⁴)/(Eh ³), where

-   -   w=deflection of plate;    -   B=shape coefficient (dependent upon length vs. width and support        of edges of plate);    -   P=applied pressure;    -   b=plate width    -   E=Young's modulus; and    -   h=plate thickness.

Thus even in this extremely simplified expression, deflection of anelastomeric membrane in response to a pressure will be a function of:the length, width, and thickness of the membrane, the flexibility of themembrane (Young's modulus), and the applied actuation force. Becauseeach of these parameters will vary widely depending upon the actualdimensions and physical composition of a particular elastomeric devicein accordance with the present invention, a wide range of membranethicknesses and elasticities, channel widths, and actuation forces arecontemplated by the present invention.

It should be understood that the formula just presented is only anapproximation, since in general the membrane does not have uniformthickness, the membrane thickness is not necessarily small compared tothe length and width, and the deflection is not necessarily smallcompared to length, width, or thickness of the membrane. Nevertheless,the equation serves as a useful guide for adjusting variable parametersto achieve a desired response of deflection versus applied force.

FIGS. 15A and 15B illustrate valve opening vs. applied pressure for a100 μm wide first flow channel 30 and a 50 μm wide second flow channel32. The membrane of this device was formed by a layer of GeneralElectric Silicones RTV 615 having a thickness of approximately 30 μm anda Young's modulus of approximately 750 kPa. FIGS. 21 a and 21 b show theextent of opening of the valve to be substantially linear over most ofthe range of applied pressures.

Air pressure was applied to actuate the membrane of the device through a10 cm long piece of plastic tubing having an outer diameter of 0.025″connected to a 25 mm piece of stainless steel hypodermic tubing with anouter diameter of 0.025″ and an inner diameter of 0.013″. This tubingwas placed into contact with the control channel by insertion into theelastomeric block in a direction normal to the control channel. Airpressure was applied to the hypodermic tubing from an external LHDAminiature solenoid valve manufactured by Lee Co.

While control of the flow of material through the device has so far beendescribed utilizing applied gas pressure, other fluids could be used.

For example, air is compressible, and thus experiences some finite delaybetween the time of application of pressure by the external solenoidvalve and the time that this pressure is experienced by the membrane. Inan alternative embodiment of the present invention, pressure could beapplied from an external source to a non-compressible fluid such aswater or hydraulic oils, resulting in a near-instantaneous transfer ofapplied pressure to the membrane. However, if the displaced volume ofthe valve is large or the control channel is narrow, higher viscosity ofa control fluid may contribute to delay in actuation. The optimal mediumfor transferring pressure will therefore depend upon the particularapplication and device configuration, and both gaseous and liquid mediaare contemplated by the invention.

While external applied pressure as described above has been applied by apump/tank system through a pressure regulator and external miniaturevalve, other methods of applying external pressure are also contemplatedin the present invention, including gas tanks, compressors, pistonsystems, and columns of liquid. Also contemplated is the use ofnaturally occurring pressure sources such as may be found inside livingorganisms, such as blood pressure, gastric pressure, the pressurepresent in the cerebro-spinal fluid, pressure present in theintra-ocular space, and the pressure exerted by muscles during normalflexure. Other methods of regulating external pressure are alsocontemplated, such as miniature valves, pumps, macroscopic peristalticpumps, pinch valves, and other types of fluid regulating equipment suchas is known in the art.

As can be seen, the response of valves in accordance with embodiments ofthe present invention have been experimentally shown to be almostperfectly linear over a large portion of its range of travel, withminimal hysteresis. Accordingly, the present valves are ideally suitedfor microfluidic metering and fluid control. The linearity of the valveresponse demonstrates that the individual valves are well modeled asHooke's Law springs. Furthermore, high pressures in the flow channel(i.e.: back pressure) can be countered simply by increasing theactuation pressure. Experimentally, the present inventors have achievedvalve closure at back pressures of 70 kPa, but higher pressures are alsocontemplated. The following is a nonexclusive list of pressure rangesencompassed by the present invention: 10 Pa-25 MPa; 100 Pa-10 Mpa, 1kPa-1 MPa, 1 kPa-300 kPa, 5 kPa-200 kPa, and 15 kPa-100 kPa.

While valves and pumps do not require linear actuation to open andclose, linear response does allow valves to more easily be used asmetering devices. In one embodiment of the invention, the opening of thevalve is used to control flow rate by being partially actuated to aknown degree of closure. Linear valve actuation makes it easier todetermine the amount of actuation force required to close the valve to adesired degree of closure. Another benefit of linear actuation is thatthe force required for valve actuation may be easily determined from thepressure in the flow channel. If actuation is linear, increased pressurein the flow channel may be countered by adding the same pressure (forceper unit area) to the actuated portion of the valve.

Linearity of a valve depends on the structure, composition, and methodof actuation of the valve structure. Furthermore, whether linearity is adesirable characteristic in a valve depends on the application.Therefore, both linearly and nonlinearly actuable valves arecontemplated in the present invention, and the pressure ranges overwhich a valve is linearly actuable will vary with the specificembodiment.

FIG. 16 illustrates time response (i.e.: closure of valve as a functionof time in response to a change in applied pressure) of a 100 μm×100μm×100 μm RTV microvalve with 10-cm-long air tubing connected from thechip to a pneumatic valve as described above.

Two periods of digital control signal, actual air pressure at the end ofthe tubing and valve opening are shown in FIG. 16. The pressure appliedon the control line is 100 kPa, which is substantially higher than the40 kPa required to close the valve. Thus, when closing, the valve ispushed closed with a pressure 60 kPa greater than required. Whenopening, however, the valve is driven back to its rest position only byits own spring force (.1toreq.40 kPa). Thus, τ_(close) is expected to besmaller than τ_(open). There is also a lag between the control signaland control pressure response, due to the limitations of the miniaturevalve used to control the pressure. Calling such lags t and the 1/e timeconstants τ, the values are: τ_(open)=3.63 ms, τ_(open)=1.88 ms,τ_(close)=2.15 ms, τ_(close)=0.51 ms. If 3τ each are allowed for openingand closing, the valve runs comfortably at 75 Hz when filled withaqueous solution.

If one used another actuation method which did not suffer from openingand closing lag, this valve would run at about 375 Hz. Note also thatthe spring constant can be adjusted by changing the membrane thickness;this allows optimization for either fast opening or fast closing. Thespring constant could also be adjusted by changing the elasticity(Young's modulus) of the membrane, as is possible by introducing dopantinto the membrane or by utilizing a different elastomeric material toserve as the membrane (described above in conjunction with FIGS.14C-14H.).

When experimentally measuring the valve properties as illustrated inFIG. 16 the valve opening was measured by fluorescence. In theseexperiments, the flow channel was filled with a solution of fluoresceinisothiocyanate (FITC) in buffer (pH 8) and the fluorescence of a squarearea occupying the center .about. ⅓rd of the channel is monitored on anepi-fluorescence microscope with a photomultiplier tube with a 10 kHzbandwidth. The pressure was monitored with a Wheatstone-bridge pressuresensor (SenSym SCC15GD2) pressurized simultaneously with the controlline through nearly identical pneumatic connections.

6. Flow Channel Cross Sections

The flow channels of the present invention may optionally be designedwith different cross sectional sizes and shapes, offering differentadvantages, depending upon their desired application. For example, thecross sectional shape of the lower flow channel may have a curved uppersurface, either along its entire length or in the region disposed underan upper cross channel). Such a curved upper surface facilitates valvesealing, as follows.

Referring to FIG. 17, a cross sectional view (similar to that of FIG.14B) through flow channels 30 and 32 is shown. As can be seen, flowchannel 30 is rectangular in cross sectional shape. In an alternatepreferred aspect of the invention, as shown in FIG. 27, thecross-section of a flow channel 30 instead has an upper curved surface.

Referring first to FIG. 17, when flow channel 32 is pressurized, themembrane portion 25 of elastomeric block 24 separating flow channels 30and 32 will move downwardly to the successive positions shown by thedotted lines 25A, 25B, 25C, 25D, and 25E. As can be seen, incompletesealing may possibly result at the edges of flow channel 30 adjacentplanar substrate 14.

In the alternate preferred embodiment of FIG. 18, flow channel 30 a hasa curved upper wall 25A. When flow channel 32 is pressurized, membraneportion 25 will move downwardly to the successive positions shown bydotted lines 25A2, 25A3, 25A4 and 25A5, with edge portions of themembrane moving first into the flow channel, followed by top membraneportions. An advantage of having such a curved upper surface at membrane25A is that a more complete seal will be provided when flow channel 32is pressurized. Specifically, the upper wall of the flow channel 30 willprovide a continuous contacting edge against planar substrate 14,thereby avoiding the “island” of contact seen between wall 25 and thebottom of flow channel 30 in FIG. 17.

Another advantage of having a curved upper flow channel surface atmembrane 25A is that the membrane can more readily conform to the shapeand volume of the flow channel in response to actuation. Specifically,where a rectangular flow channel is employed, the entire perimeter (2×flow channel height, plus the flow channel width) must be forced intothe flow channel. However where an arched flow channel is used, asmaller perimeter of material (only the semi-circular arched portion)must be forced into the channel. In this manner, the membrane requiresless change in perimeter for actuation and is therefore more responsiveto an applied actuation force to block the flow channel.

In an alternate aspect, (not illustrated), the bottom of flow channel 30is rounded such that its curved surface mates with the curved upper wall25A as seen in FIG. 27 described above.

In summary, the actual conformational change experienced by the membraneupon actuation will depend upon the configuration of the particularelastomeric structure. Specifically, the conformational change willdepend upon the length, width, and thickness profile of the membrane,its attachment to the remainder of the structure, and the height, width,and shape of the flow and control channels and the material propertiesof the elastomer used. The conformational change may also depend uponthe method of actuation, as actuation of the membrane in response to anapplied pressure will vary somewhat from actuation in response to amagnetic or electrostatic force.

Moreover, the desired conformational change in the membrane will alsovary depending upon the particular application for the elastomericstructure. In the simplest embodiments described above, the valve mayeither be open or closed, with metering to control the degree of closureof the valve. In other embodiments however, it may be desirable to alterthe shape of the membrane and/or the flow channel in order to achievemore complex flow regulation. For instance, the flow channel could beprovided with raised protrusions beneath the membrane portion, such thatupon actuation the membrane shuts off only a percentage of the flowthrough the flow channel, with the percentage of flow blockedinsensitive to the applied actuation force.

Many membrane thickness profiles and flow channel cross-sections arecontemplated by the present invention, including rectangular,trapezoidal, circular, ellipsoidal, parabolic, hyperbolic, andpolygonal, as well as sections of the above shapes. More complexcross-sectional shapes, such as the embodiment with protrusionsdiscussed immediately above or an embodiment having concavities in theflow channel, are also contemplated by the present invention.

In addition, while the invention is described primarily above inconjunction with an embodiment wherein the walls and ceiling of the flowchannel are formed from elastomer, and the floor of the channel isformed from an underlying substrate, the present invention is notlimited to this particular orientation. Walls and floors of channelscould also be formed in the underlying substrate, with only the ceilingof the flow channel constructed from elastomer. This elastomer flowchannel ceiling would project downward into the channel in response toan applied actuation force, thereby controlling the flow of materialthrough the flow channel. In general, monolithic elastomer structures asdescribed elsewhere in the instant application are preferred formicrofluidic applications. However, it may be useful to employ channelsformed in the substrate where such an arrangement provides advantages.For instance, a substrate including optical waveguides could beconstructed so that the optical waveguides direct light specifically tothe side of a microfluidic channel.

7. Alternate Valve Actuation Techniques

In addition to pressure based actuation systems described above,optional electrostatic and magnetic actuation systems are alsocontemplated, as follows.

Electrostatic actuation can be accomplished by forming oppositelycharged electrodes (which will tend to attract one another when avoltage differential is applied to them) directly into the monolithicelastomeric structure. For example, referring to FIG. 14B, an optionalfirst electrode 70 (shown in phantom) can be positioned on (or in)membrane 25 and an optional second electrode 72 (also shown in phantom)can be positioned on (or in) planar substrate 14. When electrodes 70 and72 are charged with opposite polarities, an attractive force between thetwo electrodes will cause membrane 25 to deflect downwardly, therebyclosing the “valve” (i.e.: closing flow channel 30).

For the membrane electrode to be sufficiently conductive to supportelectrostatic actuation, but not so mechanically stiff so as to impedethe valve's motion, a sufficiently flexible electrode must be providedin or over membrane 25. Such an electrode may be provided by a thinmetallization layer, doping the polymer with conductive material, ormaking the surface layer out of a conductive material.

In an exemplary aspect, the electrode present at the deflecting membranecan be provided by a thin metallization layer which can be provided, forexample, by sputtering a thin layer of metal such as 20 nm of gold. Inaddition to the formation of a metallized membrane by sputtering, othermetallization approaches such as chemical epitaxy, evaporation,electroplating, and electroless plating are also available. Physicaltransfer of a metal layer to the surface of the elastomer is alsoavailable, for example by evaporating a metal onto a flat substrate towhich it adheres poorly, and then placing the elastomer onto the metaland peeling the metal off of the substrate.

A conductive electrode 70 may also be formed by depositing carbon black(i.e. Cabot Vulcan XC72R) on the elastomer surface, either by wiping onthe dry powder or by exposing the elastomer to a suspension of carbonblack in a solvent which causes swelling of the elastomer, (such as achlorinated solvent in the case of PDMS). Alternatively, the electrode70 may be formed by constructing the entire layer 20 out of elastomerdoped with conductive material (i.e. carbon black or finely dividedmetal particles). Yet further alternatively, the electrode may be formedby electrostatic deposition, or by a chemical reaction that producescarbon. In experiments conducted by the present inventors, conductivitywas shown to increase with carbon black concentration from 5.6×10⁻¹⁶ toabout 5×10⁻³ (Ω-cm)⁻¹. The lower electrode 72, which is not required tomove, may be either a compliant electrode as described above, or aconventional electrode such as evaporated gold, a metal plate, or adoped semiconductor electrode.

Magnetic actuation of the flow channels can be achieved by fabricatingthe membrane separating the flow channels with a magneticallypolarizable material such as iron, or a permanently magnetized materialsuch as polarized NdFeB. In experiments conducted by the presentinventors, magnetic silicone was created by the addition of iron powder(about 1 um particle size), up to 20% iron by weight.

Where the membrane is fabricated with a magnetically polarizablematerial, the membrane can be actuated by attraction in response to anapplied magnetic field Where the membrane is fabricated with a materialcapable of maintaining permanent magnetization, the material can firstbe magnetized by exposure to a sufficiently high magnetic field, andthen actuated either by attraction or repulsion in response to thepolarity of an applied inhomogenous magnetic field.

The magnetic field causing actuation of the membrane can be generated ina variety of ways. In one embodiment, the magnetic field is generated byan extremely small inductive coil formed in or proximate to theelastomer membrane. The actuation effect of such a magnetic coil wouldbe localized, allowing actuation of individual pump and/or valvestructures. Alternatively, the magnetic field could be generated by alarger, more powerful source, in which case actuation would be globaland would actuate multiple pump and/or valve structures at one time.

It is also possible to actuate the device by causing a fluid flow in thecontrol channel based upon the application of thermal energy, either bythermal expansion or by production of gas from liquid. For example, inone alternative embodiment in accordance with the present invention, apocket of fluid (e.g. in a fluid-filled control channel) is positionedover the flow channel. Fluid in the pocket can be in communication witha temperature variation system, for example a heater. Thermal expansionof the fluid, or conversion of material from the liquid to the gasphase, could result in an increase in pressure, closing the adjacentflow channel. Subsequent cooling of the fluid would relieve pressure andpermit the flow channel to open.

8. Networked Systems

FIGS. 19A and 19B show a views of a single on/off valve, identical tothe systems set forth above, (for example in FIG. 14A). FIGS. 20A and20B shows a peristaltic pumping system comprised of a plurality of thesingle addressable on/off valves as seen in FIG. 19, but networkedtogether. FIG. 21 is a graph showing experimentally achieved pumpingrates vs. frequency for the peristaltic pumping system of FIG. 20. FIGS.22A and 22B show a schematic view of a plurality of flow channels whichare controllable by a single control line. This system is also comprisedof a plurality of the single addressable on/off valves of FIG. 19,multiplexed together, but in a different arrangement than that of FIG.19. FIG. 23 is a schematic illustration of a multiplexing system adaptedto permit fluid flow through selected channels, comprised of a pluralityof the single on/off valves of FIG. 19, joined or networked together.

Referring first to FIGS. 19A and 19B, a schematic of flow channels 30and 32 is shown. Flow channel 30 preferably has a fluid (or gas) flow Fpassing therethrough. Flow channel 32, (which crosses over flow channel30, as was already explained herein), is pressurized such that membrane25 separating the flow channels may be depressed into the path of flowchannel 30, shutting off the passage of flow F therethrough, as has beenexplained. As such, “flow channel” 32 can also be referred to as a“control line” which actuates a single valve in flow channel 30. InFIGS. 19 to 22, a plurality of such addressable valves are joined ornetworked together in various arrangements to produce pumps, capable ofperistaltic pumping, and other fluidic logic applications.

Referring to FIGS. 20A and 20B, a system for peristaltic pumping isprovided, as follows. A flow channel 30 has a plurality of generallyparallel flow channels (i.e.: control lines) 32A, 32B and 32C passingthereover. By pressurizing control line 32A, flow F through flow channel30 is shut off under membrane 25A at the intersection of control line32A and flow channel 30. Similarly, (but not shown), by pressurizingcontrol line 32B, flow F through flow channel 30 is shut off undermembrane 25B at the intersection of control line 32B and flow channel30, etc.

Each of control lines 32A, 32B, and 32C is separately addressable.Therefore, peristalsis may be actuated by the pattern of actuating 32Aand 32C together, followed by 32A, followed by 32A and 32B together,followed by 32B, followed by 32B and C together, etc. This correspondsto a successive “101, 100, 110, 010, 011, 001” pattern, where “0”indicates “valve open” and “1” indicates “valve closed.” Thisperistaltic pattern is also known as a 120° pattern (referring to thephase angle of actuation between three valves). Other peristalticpatterns are equally possible, including 60° and 90° patterns.

In experiments performed by the inventors, a pumping rate of 2.35 nL/swas measured by measuring the distance traveled by a column of water inthin (0.5 mm i.d.) tubing; with 100×1100×10 μm valves under an actuationpressure of 40 kPa. The pumping rate increased with actuation frequencyuntil approximately 75 Hz, and then was nearly constant until above 200Hz. The valves and pumps are also quite durable and the elastomermembrane, control channels, or bond have never been observed to fail. Inexperiments performed by the inventors, none of the valves in theperistaltic pump described herein show any sign of wear or fatigue aftermore than 4 million actuations. In addition to their durability, theyare also gentle. A solution of E. coli pumped through a channel andtested for viability showed a 94% survival rate.

FIG. 21 is a graph showing experimentally achieved pumping rates vs.frequency for the peristaltic pumping system of FIG. 20.

FIGS. 22A and 22B illustrates another way of assembling a plurality ofthe addressable valves of FIG. 19. Specifically, a plurality of parallelflow channels 30A, 30B, and 30C are provided. Flow channel (i.e.:control line) 32 passes thereover across flow channels 30A, 30B, and30C. Pressurization of control line 32 simultaneously shuts off flowsF1, F2 and F3 by depressing membranes 25A, 25B, and 25C located at theintersections of control line 32 and flow channels 30A, 30B, and 30C.

FIG. 23 is a schematic illustration of a multiplexing system adapted toselectively permit fluid to flow through selected channels, as follows.The downward deflection of membranes separating the respective flowchannels from a control line passing thereabove (for example, membranes25A, 25B, and 25C in FIGS. 22A and 22B) depends strongly upon themembrane dimensions. Accordingly, by varying the widths of flow channelcontrol line 32 in FIGS. 22A and 22B, it is possible to have a controlline pass over multiple flow channels, yet only actuate (i.e.: seal)desired flow channels. FIG. 23 illustrates a schematic of such a system,as follows.

A plurality of parallel flow channels 30A, 30B, 30C, 30D, 30E and 30Fare positioned under a plurality of parallel control lines 32A, 32B,32C, 32D, 32E and 32F. Control channels 32A, 32B, 32C, 32D, 32E and 32Fare adapted to shut off fluid flows F1, F2, F3, F4, F5 and F6 passingthrough parallel flow channels 30A, 30B, 30C, 30D, 30E and 30F using anyof the valving systems described above, with the following modification.

Each of control lines 32A, 32B, 32C, 32D, 32E and 32F have both wide andnarrow portions. For example, control line 32A is wide in locationsdisposed over flow channels 30A, 30C and 30E. Similarly, control line32B is wide in locations disposed over flow channels 30B, 30D and 30F,and control line 32C is wide in locations disposed over flow channels30A, 30B, 30E and 30F.

At the locations where the respective control line is wide, itspressurization will cause the membrane (25) separating the flow channeland the control line to depress significantly into the flow channel,thereby blocking the flow passage therethrough. Conversely, in thelocations where the respective control line is narrow, membrane (25)will also be narrow. Accordingly, the same degree of pressurization willnot result in membrane (25) becoming depressed into the flow channel(30). Therefore, fluid passage thereunder will not be blocked.

For example, when control line 32A is pressurized, it will block flowsF1, F3 and F5 in flow channels 30A, 30C and 30E. Similarly, when controlline 32C is pressurized, it will block flows F1, F2, F5 and F6 in flowchannels 30A, 30B, 30E and 30F. As can be appreciated, more than onecontrol line can be actuated at the same time. For example, controllines 32A and 32C can be pressurized simultaneously to block all fluidflow except F4 (with 32A blocking F1, F3 and F5; and 32C blocking F1,F2, F5 and F6).

By selectively pressurizing different control lines (32) both togetherand in various sequences, a great degree of fluid flow control can beachieved. Moreover, by extending the present system to more than sixparallel flow channels (30) and more than four parallel control lines(32), and by varying the positioning of the wide and narrow regions ofthe control lines, very complex fluid flow control systems may befabricated. A property of such systems is that it is possible to turn onany one flow channel out of n flow channels with only 2(log₂n) controllines.

9. Selectively Addressable Reaction Chambers Along Flow Lines

In a further embodiment of the invention, illustrated in FIGS. 26A, 26B,26C and 26D, a system for selectively directing fluid flow into one moreof a plurality of reaction chambers disposed along a flow line isprovided.

FIG. 26A shows a top view of a flow channel 30 having a plurality ofreaction chambers 80A and 80B disposed therealong. Preferably flowchannel 30 and reaction chambers 80A and 80B are formed together asrecesses into the bottom surface of a first layer 100 of elastomer.

FIG. 26B shows a bottom plan view of another elastomeric layer 110 withtwo control lines 32A and 32B each being generally narrow, but havingwide extending portions 33A and 33B formed as recesses therein.

As seen in the exploded view of FIG. 26C, and assembled view of FIG.26D, elastomeric layer 110 is placed over elastomeric layer 100. Layers100 and 110 are then bonded together, and the integrated system operatesto selectively direct fluid flow F (through flow channel 30) into eitheror both of reaction chambers 80A and 80B, as follows. Pressurization ofcontrol line 32A will cause the membrane 25 (i.e.: the thin portion ofelastomer layer 100 located below extending portion 33A and over regions82A of reaction chamber 80A) to become depressed, thereby shutting offfluid flow passage in regions 82A, effectively sealing reaction chamber80 from flow channel 30. As can also be seen, extending portion 33A iswider than the remainder of control line 32A. As such, pressurization ofcontrol line 32A will not result in control line 32A sealing flowchannel 30.

As can be appreciated, either or both of control lines 32A and 32B canbe actuated at once. When both control lines 32A and 32B are pressurizedtogether, sample flow in flow channel 30 will enter neither of reactionchambers 80A or 80B.

The concept of selectably controlling fluid introduction into variousaddressable reaction chambers disposed along a flow line (FIGS. 24A-D)can be combined with concept of selectably controlling fluid flowthrough one or more of a plurality of parallel flow lines (FIG. 23) toyield a system in which a fluid sample or samples can be can be sent toany particular reaction chamber in an array of reaction chambers. Anexample of such a system is provided in FIG. 25, in which parallelcontrol channels 32A, 32B and 32C with extending portions 34 (all shownin phantom) selectively direct fluid flows F1 and F2 into any of thearray of reaction wells 80A, 80B, 80C or 80D as explained above; whilepressurization of control lines 32C and 32D selectively shuts off flowsF2 and F1, respectively.

In yet another novel embodiment, fluid passage between parallel flowchannels is possible. Referring to FIG. 26, either or both of controllines 32A or 32D can be depressurized such that fluid flow throughlateral passageways 35 (between parallel flow channels 30A and 30B) ispermitted. In this aspect of the invention, pressurization of controllines 32C and 32D would shut flow channel 30A between 35A and 35B, andwould also shut lateral passageways 35B. As such, flow entering as flowF1 would sequentially travel through 30A, 35A and leave 30B as flow F4.

10. Switchable Flow Arrays

In yet another novel embodiment, fluid passage can be selectivelydirected to flow in either of two perpendicular directions. An exampleof such a “switchable flow array” system is provided in FIGS. 27A to27D. FIG. 27A shows a bottom view of a first layer of elastomer 90, (orany other suitable substrate), having a bottom surface with a pattern ofrecesses forming a flow channel grid defined by an array of solid posts92, each having flow channels passing therearound.

In preferred aspects, an additional layer of elastomer is bound to thetop surface of layer 90 such that fluid flow can be selectively directedto move either in direction F1, or perpendicular direction F2. FIG. 27is a bottom view of the bottom surface of the second layer of elastomer95 showing recesses formed in the shape of alternating “vertical”control lines 96 and “horizontal” control lines 94. “Vertical” controllines 96 have the same width therealong, whereas “horizontal” controllines 94 have alternating wide and narrow portions, as shown.

Elastomeric layer 95 is positioned over top of elastomeric layer 90 suchthat “vertical” control lines 96 are positioned over posts 92 as shownin FIG. 27C and “horizontal” control lines 94 are positioned with theirwide portions between posts 92, as shown in FIG. 27D.

As can be seen in FIG. 27C, when “vertical” control lines 96 arepressurized, the membrane of the integrated structure formed by theelastomeric layer initially positioned between layers 90 and 95 inregions 98 will be deflected downwardly over the array of flow channelssuch that flow in only able to pass in flow direction F2 (i.e.:vertically), as shown.

As can be seen in FIG. 27D, when “horizontal” control lines 94 arepressurized, the membrane of the integrated structure formed by theelastomeric layer initially positioned between layers 90 and 95 inregions 99 will be deflected downwardly over the array of flow channels,(but only in the regions where they are widest), such that flow in onlyable to pass in flow direction F1 (i.e.: horizontally), as shown.

The design illustrated in FIG. 27 allows a switchable flow array to beconstructed from only two elastomeric layers, with no vertical viaspassing between control lines in different elastomeric layers required.If all vertical flow control lines 94 are connected, they may bepressurized from one input. The same is true for all horizontal flowcontrol lines 96.

11. Normally-Closed Valve Structure

FIGS. 14B and 14H above depict a valve structure in which theelastomeric membrane is moveable from a first relaxed position to asecond actuated position in which the flow channel is blocked. However,the present invention is not limited to this particular valveconfiguration.

FIGS. 28A-28J show a variety of views of a normally-closed valvestructure in which the elastomeric membrane is moveable from a firstrelaxed position blocking a flow channel, to a second actuated positionin which the flow channel is open, utilizing a negative controlpressure.

FIG. 28A shows a plan view, and FIG. 28B shows a cross sectional viewalong line 42B-42B′, of normally-closed valve 4200 in an unactuatedstate. Flow channel 4202 and control channel 4204 are formed inelastomeric block 4206 overlying substrate 4205. Flow channel 4202includes a first portion 4202 a and a second portion 4202 b separated byseparating portion 4208. Control channel 4204 overlies separatingportion 4208. As shown in FIG. 28B, in its relaxed, unactuated position,separating portion 4008 remains positioned between flow channel portions4202 a and 4202 b, interrupting flow channel 4202.

FIG. 28C shows a cross-sectional view of valve 4200 wherein separatingportion 4208 is in an actuated position. When the pressure withincontrol channel 4204 is reduced to below the pressure in the flowchannel (for example by vacuum pump), separating portion 4208experiences an actuating force drawing it into control channel 4204. Asa result of this actuation force membrane 4208 projects into controlchannel 4204, thereby removing the obstacle to a flow of materialthrough flow channel 4202 and creating a passageway 4203. Upon elevationof pressure within control channel 4204, separating portion 4208 willassume its natural position, relaxing back into and obstructing flowchannel 4202.

The behavior of the membrane in response to an actuation force may bechanged by varying the width of the overlying control channel.Accordingly, FIGS. 28D-28H show plan and cross-sectional views of analternative embodiment of a normally-closed valve 4201 in which controlchannel 4207 is substantially wider than separating portion 4208. Asshown in cross-sectional views FIG. 28E-F along line 42E-42E′ of FIG.28D, because a larger area of elastomeric material is required to bemoved during actuation, the actuation force necessary to be applied isreduced.

FIGS. 28G and H show a cross-sectional views along line 40G-40G′ of FIG.21D. In comparison with the unactuated valve configuration shown in FIG.28G, FIG. 28H shows that reduced pressure within wider control channel4207 may under certain circumstances have the unwanted effect of pullingunderlying elastomer 4206 away from substrate 4205, thereby creatingundesirable void 4212.

Accordingly, FIG. 28I shows a plan view, and FIG. 28J shows across-sectional view along line 21J-21J′ of FIG. 28I, of valve structure4220 which avoids this problem by featuring control line 4204 with aminimum width except in segment 4204 a overlapping separating portion4208. As shown in FIG. 28J, even under actuated conditions the narrowercross-section of control channel 4204 reduces the attractive force onthe underlying elastomer material 4206, thereby preventing thiselastomer material from being drawn away from substrate 4205 andcreating an undesirable void.

While a normally-closed valve structure actuated in response to pressureis shown in FIGS. 28A-28J, a normally-closed valve in accordance withthe present invention is not limited to this configuration. For example,the separating portion obstructing the flow channel could alternativelybe manipulated by electric or magnetic fields, as described extensivelyabove.

12. Side-Actuated Valve

While the above description has focused upon microfabricated elastomericvalve structures in which a control channel is positioned above andseparated by an intervening elastomeric membrane from an underlying flowchannel, the present invention is not limited to this configuration.FIGS. 29A and 29B show plan views of one embodiment of a side-actuatedvalve structure in accordance with one embodiment of the presentinvention.

FIG. 29A shows side-actuated valve structure 4800 in an unactuatedposition. Flow channel 4802 is formed in elastomeric layer 4804. Controlchannel 4806 abutting flow channel 4802 is also formed in elastomericlayer 4804. Control channel 4806 is separated from flow channel 4802 byelastomeric membrane portion 4808. A second elastomeric layer (notshown) is bonded over bottom elastomeric layer 4804 to enclose flowchannel 4802 and control channel 4806.

FIG. 29B shows side-actuated valve structure 4800 in an actuatedposition. In response to a build up of pressure within control channel4806, membrane 4808 deforms into flow channel 4802, blocking flowchannel 4802. Upon release of pressure within control channel 4806,membrane 4808 would relax back into control channel 4806 and open flowchannel 4802.

While a side-actuated valve structure actuated in response to pressureis shown in FIGS. 29A and 29B, a side-actuated valve in accordance withthe present invention is not limited to this configuration. For example,the elastomeric membrane portion located between the abutting flow andcontrol channels could alternatively be manipulated by electric ormagnetic fields, as described extensively above.

13. Composite Structures

Microfabricated elastomeric structures of the present invention may becombined with non-elastomeric materials to create composite structures.FIG. 30 shows a cross-sectional view of one embodiment of a compositestructure in accordance with the present invention. FIG. 30 showscomposite valve structure 5700 including first, thin elastomer layer5702 overlying semiconductor-type substrate 5704 having channel 5706formed therein. Second, thicker elastomer layer 5708 overlies firstelastomer layer 5702. Actuation of first elastomer layer 5702 to driveit into channel 5706, will cause composite structure 5700 to operate asa valve.

FIG. 31 shows a cross-sectional view of a variation on this theme,wherein thin elastomer layer 5802 is sandwiched between two hard,semiconductor substrates 5804 and 5806, with lower substrate 5804featuring channel 5808. Again, actuation of thin elastomer layer 5802 todrive it into channel 5808 will cause composite structure 5810 tooperate as a valve.

The structures shown in FIG. 30 or 31 may be fabricated utilizing eitherthe multilayer soft lithography or encapsulation techniques describedabove. In the multilayer soft lithography method, the elastomer layer(s)would be formed and then placed over the semiconductor substrate bearingthe channel. In the encapsulation method, the channel would be firstformed in the semiconductor substrate, and then the channel would befilled with a sacrificial material such as photoresist. The elastomerwould then be formed in place over the substrate, with removal of thesacrificial material producing the channel overlaid by the elastomermembrane. As is discussed in detail below in connection with bonding ofelastomer to other types of materials, the encapsulation approach mayresult in a stronger seal between the elastomer membrane component andthe underlying nonelastomer substrate component.

As shown in FIGS. 30 and 31, a composite structure in accordance withembodiments of the present invention may include a hard substrate thatbears a passive feature such as a channels. However, the presentinvention is not limited to this approach, and the underlying hardsubstrate may bear active features that interact with an elastomercomponent bearing a recess. This is shown in FIG. 32, wherein compositestructure 5900 includes elastomer component 5902 containing recess 5904having walls 5906 and ceiling 5908. Ceiling 5908 forms flexible membraneportion 5909. Elastomer component 5902 is sealed against substantiallyplanar nonelastomeric component 5910 that includes active device 5912.Active device 5912 may interact with material present in recess 5904and/or flexible membrane portion 5909.

Many Types of active structures may be present in the nonelastomersubstrate. Active structures that could be present in an underlying hardsubstrate include, but are not limited to, resistors, capacitors,photodiodes, transistors, chemical field effect transistors (chemFET's), amperometric/coulometric electrochemical sensors, fiber optics,fiber optic interconnects, light emitting diodes, laser diodes, verticalcavity surface emitting lasers (VCSEL's), micromirrors, accelerometers,pressure sensors, flow sensors, CMOS imaging arrays, CCD cameras,electronic logic, microprocessors, thermistors, Peltier coolers,waveguides, resistive heaters, chemical sensors, strain gauges,inductors, actuators (including electrostatic, magnetic,electromagnetic, bimetallic, piezoelectric, shape-memory-alloy based,and others), coils, magnets, electromagnets, magnetic sensors (such asthose used in hard drives, superconducting quantum interference devices(SQUIDS) and other types), radio frequency sources and receivers,microwave frequency sources and receivers, sources and receivers forother regions of the electromagnetic spectrum, radioactive particlecounters, and electrometers.

As is well known in the art, a vast variety of technologies can beutilized to fabricate active features in semiconductor and other typesof hard substrates, including but not limited printed circuit board(PCB) technology, CMOS, surface micromachining, bulk micromachining,printable polymer electronics, and TFT and otheramorphous/polycrystalline techniques as are employed to fabricate laptopand flat screen displays.

A variety of approaches can be employed to seal the elastomericstructure against the nonelastomeric substrate, ranging from thecreation of a Van der Waals bond between the elastomeric andnonelastomeric components, to creation of covalent or ionic bondsbetween the elastomeric and nonelastomeric components of the compositestructure. Example approaches to sealing the components together arediscussed below, approximately in order of increasing strength.

A first approach is to rely upon the simple hermetic seal resulting fromVan der Waals bonds formed when a substantially planar elastomer layeris placed into contact with a substantially planar layer of a harder,non-elastomer material. In one embodiment, bonding of RTV elastomer to aglass substrate created a composite structure capable of withstanding upto about 3-4 psi of pressure. This may be sufficient for many potentialapplications.

A second approach is to utilize a liquid layer to assist in bonding. Oneexample of this involves bonding elastomer to a hard glass substrate,wherein a weakly acidic solution (5 μl HCl in H₂O, pH 2) was applied toa glass substrate. The elastomer component was then placed into contactwith the glass substrate, and the composite structure baked at 37° C. toremove the water. This resulted in a bond between elastomer andnon-elastomer able to withstand a pressure of about 20 psi. In thiscase, the acid may neutralize silanol groups present on the glasssurface, permitting the elastomer and nonelastomer to enter into goodVan der Waals contact with each other.

Exposure to ethanol can also cause device components to adhere together.In one embodiment, an RTV elastomer material and a glass substrate werewashed with ethanol and then dried under Nitrogen. The RTV elastomer wasthen placed into contact with the glass and the combination baked for 3hours at 80° C. Optionally, the RTV may also be exposed to a vacuum toremove any air bubbles trapped between the slide and the RTV. Thestrength of the adhesion between elastomer and glass using this methodhas withstood pressures in excess of 35 psi. The adhesion created usingthis method is not permanent, and the elastomer may be peeled off of theglass, washed, and resealed against the glass. This ethanol washingapproach can also be employed used to cause successive layers ofelastomer to bond together with sufficient strength to resist a pressureof 30 psi. In alternative embodiments, chemicals such as other alcoholsor diols could be used to promote adhesion between layers.

An embodiment of a method of promoting adhesion between layers of amicrofabricated structure in accordance with the present inventioncomprises exposing a surface of a first component layer to a chemical,exposing a surface of a second component layer to the chemical, andplacing the surface of the first component layer into contact with thesurface of the second elastomer layer.

A third approach is to create a covalent chemical bond between theelastomer component and functional groups introduced onto the surface ofa nonelastomer component. Examples of derivitization of a nonelastomersubstrate surface to produce such functional groups include exposing aglass substrate to agents such as vinyl silane or aminopropyltriethoxysilane (APTES), which may be useful to allow bonding of the glass tosilicone elastomer and polyurethane elastomer materials, respectively.

A fourth approach is to create a covalent chemical bond between theelastomer component and a functional group native to the surface of thenonelastomer component. For example, RTV elastomer can be created withan excess of vinyl groups on its surface. These vinyl groups can becaused to react with corresponding functional groups present on theexterior of a hard substrate material, for example the Si—H bondsprevalent on the surface of a single crystal silicon substrate afterremoval of native oxide by etching. In this example, the strength of thebond created between the elastomer component and the nonelastomercomponent has been observed to exceed the materials strength of theelastomer components.

14. Cell Pen/Cell Cage

In yet a further application of the present invention, an elastomericstructure can be utilized to manipulate organisms or other biologicalmaterial. FIGS. 33A-33D show plan views of one embodiment of a cell penstructure in accordance with the present invention.

Cell pen array 4400 features an array of orthogonally-oriented flowchannels 4402, with an enlarged “pen” structure 4404 at the intersectionof alternating flow channels. Valve 4406 is positioned at the entranceand exit of each pen structure 4404. Peristaltic pump structures 4408are positioned on each horizontal flow channel and on the vertical flowchannels lacking a cell pen structure.

Cell pen array 4400 of FIG. 33A has been loaded with cells A-H that havebeen previously sorted. FIGS. 33B-33C show the accessing and removal ofindividually stored cell C by 1) opening valves 4406 on either side ofadjacent pens 4404 a and 4404 b, 2) pumping horizontal flow channel 4402a to displace cells C and G, and then 3) pumping vertical flow channel4402 b to remove cell C. FIG. 33D shows that second cell G is moved backinto its prior position in cell pen array 4400 by reversing thedirection of liquid flow through horizontal flow channel 4402 a.

The cell pen array 4404 described above is capable of storing materialswithin a selected, addressable position for ready access. However,living organisms such as cells may require a continuous intake of foodsand expulsion of wastes in order to remain viable. Accordingly, FIGS.34A and 34B show plan and cross-sectional views (along line 45B-45B′)respectively, of one embodiment of a cell cage structure in accordancewith the present invention.

Cell cage 4500 is formed as an enlarged portion 4500 a of a flow channel4501 in an elastomeric block 4503 in contact with substrate 4505. Cellcage 4500 is similar to an individual cell pen as described above inFIGS. 33A-33D, except that ends 4500 b and 4500 c of cell cage 4500 donot completely enclose interior region 4500 a. Rather, ends 4500 a and4500 b of cage 4500 are formed by a plurality of retractable pillars4502. Pillars 4502 may be part of a membrane structure of anormally-closed valve structure as described extensively above inconnection with FIGS. 28A-28J.

Specifically, control channel 4504 overlies pillars 4502. When thepressure in control channel 4504 is reduced, elastomeric pillars 4502are drawn upward into control channel 4504, thereby opening end 4500 bof cell cage 4500 and permitting a cell to enter. Upon elevation ofpressure in control channel 4504, pillars 4502 relax downward againstsubstrate 4505 and prevent a cell from exiting cage 4500.

Elastomeric pillars 4502 are of a sufficient size and number to preventmovement of a cell out of cage 4500, but also include gaps 4508 whichallow the flow of nutrients into cage interior 4500 a in order tosustain cell(s) stored therein. Pillars 4502 on opposite end 4500 c aresimilarly configured beneath second control channel 4506 to permitopening of the cage and removal of the cell as desired.

The cross-flow channel architecture illustrated shown in FIGS. 33A-33Dcan be used to perform functions other than the cell pen just described.For example, the cross-flow channel architecture can be utilized inmixing applications.

This is shown in FIGS. 35A-B, which illustrate a plan view of mixingsteps performed by a microfabricated structure in accordance anotherembodiment of the present invention. Specifically, portion 7400 of amicrofabricated mixing structure comprises first flow channel 7402orthogonal to and intersecting with second flow channel 7404. Controlchannels 7406 overlie flow channels 7402 and 7404 and form valve pairs7408 a-b and 7408 c-d that surround each intersection 7412.

As shown in FIG. 35A, valve pair 7408 a-b is initially opened whilevalve pair 7408 c-d is closed, and fluid sample 7410 is flowed tointersection 7412 through flow channel 7402. Valve pair 7408 c-d is thenactuated, trapping fluid sample 7410 at intersection 7412.

Next, as shown in FIG. 35B, valve pairs 7408 a-b and 7408 c-d areopened, such that fluid sample 7410 is injected from intersection 7412into flow channel 7404 bearing a cross-flow of fluid. The process shownin FIGS. 35A-B can be repeated to accurately dispense any number offluid samples down cross-flow channel 7404.

While the embodiment shown and described above in connection with FIGS.35A-35B utilizes linked valve pairs on opposite sides of the flowchannel intersections, this is not required by the present invention.Other configurations, including linking of adjacent valves of anintersection, or independent actuation of each valve surrounding anintersection, are possible to provide the desired flow characteristics.With the independent valve actuation approach however, it should berecognized that separate control structures would be utilized for eachvalve, complicating device layout.

15. Metering By Volume Exclusion

Many high throughput screening and diagnostic applications call foraccurate combination and of different reagents in a reaction chamber.Given that it is frequently necessary to prime the channels of amicrofluidic device in order to ensure fluid flow, it may be difficultto ensure mixed solutions do not become diluted or contaminated by thecontents of the reaction chamber prior to sample introduction.

Volume exclusion is one technique enabling precise metering of theintroduction of fluids into a reaction chamber. In this approach, areaction chamber may be completely or partially emptied prior to sampleinjection. This method reduces contamination from residual contents ofthe chamber contents, and may be used to accurately meter theintroduction of solutions in a reaction chamber.

Specifically, FIGS. 36A-36D show cross-sectional views of a reactionchamber in which volume exclusion is employed to meter reactants. FIG.36A shows a cross-sectional view of portion 6300 of a microfluidicdevice comprising first elastomer layer 6302 overlying second elastomerlayer 6304. First elastomer layer 6302 includes control chamber 6306 influid communication with a control channel (not shown). Control chamber6306 overlies and is separated from dead-end reaction chamber 6308 ofsecond elastomer layer 6304 by membrane 6310. Second elastomer layer6304 further comprises flow channel 6312 leading to dead-end reactionchamber 6308.

FIG. 36B shows the result of a pressure increase within control chamber6306. Specifically, increased control chamber pressure causes membrane6310 to flex downward into reaction chamber 6308, reducing by volume Vthe effective volume of reaction chamber 6308. This in turn excludes anequivalent volume V of reactant from reaction chamber 6308, such thatvolume V of first reactant X is output from flow channel 6312. The exactcorrelation between a pressure increase in control chamber 6306 and thevolume of material output from flow channel 6312 can be preciselycalibrated.

As shown in FIG. 36C, while elevated pressure is maintained withincontrol chamber 6306, volume V′ of second reactant Y is placed intocontact with flow channel 6312 and reaction chamber 6308.

In the next step shown in FIG. 36D, pressure within control chamber 6306is reduced to original levels. As a result, membrane 6310 relaxes andthe effective volume of reaction chamber 6308 increases. Volume V ofsecond reactant Y is sucked into the device. By varying the relativesize of the reaction and control chambers, it is possible to accuratelymix solutions at a specified relative concentration. It is worth notingthat the amount of the second reactant Y that is sucked into the deviceis solely dependent upon the excluded volume V, and is independent ofvolume V′ of Y made available at the opening of the flow channel.

While FIGS. 36A-36D show a simple embodiment of the present inventioninvolving a single reaction chamber, in more complex embodimentsparallel structures of hundreds or thousands of reaction chambers couldbe actuated by a pressure increase in a single control line.

Moreover, while the above description illustrates two reactants beingcombined at a relative concentration that fixed by the size of thecontrol and reaction chambers, a volume exclusion technique could beemployed to combine several reagents at variable concentrations in asingle reaction chamber. One possible approach is to use several,separately addressable control chambers above each reaction chamber. Anexample of this architecture would be to have ten separate control linesinstead of a single control chamber, allowing ten equivalent volumes tobe pushed out or sucked in.

Another possible approach would utilize a single control chamberoverlying the entire reaction chamber, with the effective volume of thereaction chamber modulated by varying the control chamber pressure. Inthis manner, analog control over the effective volume of the reactionchamber is possible. Analog volume control would in turn permit thecombination of many solutions reactants at arbitrary relativeconcentrations.

An embodiment of a method of metering a volume of fluid in accordancewith the present invention comprises providing a chamber having a volumein an elastomeric block separated from a control recess by anelastomeric membrane, and supplying a pressure to the control recesssuch that the membrane is deflected into the chamber and the volume isreduced by a calibrated amount, thereby excluding from the chamber thecalibrated volume of fluid.

Having described several embodiments, it will be recognized by those ofskill in the art that various modifications, alternative constructions,and equivalents may be used without departing from the spirit of theinvention. Additionally, a number of well known processes and elementshave not been described in order to avoid unnecessarily obscuring thepresent invention. Accordingly, the above description should not betaken as limiting the scope of the invention.

Where a range of values is provided, it is understood that eachintervening value, to the tenth of the unit of the lower limit unlessthe context clearly dictates otherwise, between the upper and lowerlimits of that range is also specifically disclosed. Each smaller rangebetween any stated value or intervening value in a stated range and anyother stated or intervening value in that stated range is encompassedwithin the invention. The upper and lower limits of these smaller rangesmay independently be included or excluded in the range, and each rangewhere either, neither or both limits are included in the smaller rangesis also encompassed within the invention, subject to any specificallyexcluded limit in the stated range. Where the stated range includes oneor both of the limits, ranges excluding either or both of those includedlimits are also included in the invention.

As used herein and in the appended claims, the singular forms “a”,“and”, and “the” include plural referents unless the context clearlydictates otherwise. Thus, for example, reference to “a process” includesa plurality of such processes and reference to “the electrode” includesreference to one or more electrodes and equivalents thereof known tothose skilled in the art, and so forth.

Also, the words “comprise,” “comprising,” “include,” “including,” and“includes” when used in this specification and in the following claimsare intended to specify the presence of stated features, integers,components, or steps, but they do not preclude the presence or additionof one or more other features, integers, components, steps, or groups.

What is claimed is:
 1. A chemostat comprising: a growth chamber having aplurality of compartments, wherein each of the compartments may befluidly isolated from the rest of the growth chamber by one or moreactuatable valves; a nutrient supply-line to supply growth medium to thegrowth chamber; and an output port to remove fluids from the growthchamber.
 2. A chemostat chip comprising an array of chemostats, whereineach of the chemostats comprises: a growth chamber having a plurality ofcompartments, wherein each of the compartments may be fluidly isolatedfrom the rest of the growth chamber by one or more actuatable valves; anutrient supply-line to supply growth medium to the growth chamber; andan output port to remove fluids from the growth chamber.
 3. A method ofpreventing biofilm formation in a growth chamber of a chemostat, themethod comprising: adding a lysis agent to an isolated portion of thegrowth chamber; and reuniting the isolated portion with the rest of thegrowth chamber.